Situations where a cessationist can still expect a miracle
I am answering as a typical Concentric cessationist who, in addition, believe that the Bible is the only authoritative prophecy that applies to everyone. I also add the qualification that there is no more need for apostles acting in authority, like the 12 apostles, even in the "unreached" areas. There is only one Lord who exercises his authority in people's hearts.
The only kind of miracles that can accompany gospel preaching in "unreached" areas (as well as in revivals in "reached" areas such as the Western world) are healing, exorcism, and targeted (individual) "prophecy" (to convict someone of specific sin, cf. 1 Cor 14:24-25). To a lesser extent, there may be others as described in definition #3 of my other answer.
There is no permanent miraculous gift/charism (like the gift to heal others) given to anyone (unlike what Pentecostals teach). The Holy Spirit is free to perform these miracles through anyone (who does not have to be a missionary) to aid conversion and to increase a person's faith in Jesus Christ, especially in the "unreached" areas.
CONCLUSION: All miracles are optional, and when they do occur they have to be evaluated by the Bible as the higher authority.
Concentric cessationist vs. continuationist
"unreached areas" is admittedly a rather loose "psychographic" way to define the "unreached" (thanks, @OneGodTheFather), to be distinguished with the more common (but arguably distorted) "geographic" way, such as equating "unreached" with the Global South where Christianity has grown in numbers in the past few decades. It's distorted because many pockets of "reached areas" (such as in the Global North) have degenerated into a mission field where in fact missionaries from Brazil, Nigeria, Korea, etc. are currently working (i.e. "reverse mission").
Dr. Daniel B. Wallace (who coined the term "concentric cessationism" in his talk at the 1994 Evangelical Theological Society's regional meeting) defined it this way:
I believe that certain gifts of the Holy Spirit were employed in the earliest stage of Christianity to authenticate that God was doing something new. These "sign gifts"--such as the gifts of healing, tongues, miracles--ceased with the death of the last apostle. This is what I mean by "cessationism." Some of you fellow cessationists might style yourselves as "soft" cessationists whereby you mean that some of the sign gifts continue, or that the sign gifts may crop up in locations where the gospel is introduced afresh,1 or that you are presently agnostic about these gifts, but are not a practicing charismatic.
1 This is what I would call concentric cessationism, as opposed to linear cessationism. That is, rather than taking a chronologically linear approach, this kind of cessationism affirms that as the gospel moves, like the rippling effect of a stone dropping into a pond, in a space-time expanding circle away from first century Jerusalem, the sign gifts will still exist on the cutting edge of that circle. Thus, for example, in third world countries at the time when the gospel is first proclaimed, the sign gifts would be present. This view, then, would allow for these gifts to exist on the frontiers of Christianity, but would be more skeptical of them in the 'worked over' areas.
So how can a Christian (such as myself) meaningfully claim to be a concentric cessationist rather than a straightforward cautious continuationist (like Craig Keener)?
- I appeal to Dr. David Wallace's 11 theses in the talk above (especially #1, #2, #6, #9, #10, and #11).
- I also prioritize the Bible rather the experience alone or the subjective consciousness alone to frame and distinguish genuine "miraculous" / "supernatural" experiences from those that are not, especially for those in definition #2 degree 3, or in definition #3 in my answer on the definition of a miracle.
- When deciding whether something is a "miracle" or not,
I also give more weight to say "yes" when it occurs in connection with either a person's conversion or a person's increase of faith. For example, a straightforward cautious continuationist would not use either criteria but rather expected a miracle to occur in any contexts. Example: a continuationist who says that the Holy Spirit told her to move to another house, or that the unexpected gift from someone is a gift from God, or that she suddenly feel a lot better in her back would label that experience as a "miracle" even though during the post-miracle period there is no discernible increase in faith, while a concentric cessationist would not label that experience as miracle.
How a cessationist evaluates a miracle report
Medical report, psychological / psychiatric evaluation, detective-style investigation, etc. are secondary. We cannot say, that if it is a certifiable miracle then it must have come from God. Even in Jesus's time, there were miracles associated with other religions (hear how Jimmy Akin answered an audience's question in the 2:14:45 to 2:17:31 segment of Jimmy Akin's debate with Bart Ehrman about the Gospel authors' view of the historical supernatural claims that were not brought about by Jesus or His apostles/followers).
What is key for my evaluation is whether the new believer / the missionary has done proper Biblical-based discernment on whether the miracle was caused the Holy Spirit, by examining their fruit during some extended post-miracle period, i.e. whether the person objectively becomes a follower and a lover of Jesus Christ. For example, if a person becomes "obsessive" in expecting a miracle rather than Christ (see below), then there is an indication that the Holy Spirit wasn't behind the "miracle". Or if the person later does not stay a Christian, then the "miracle" probably wasn't a genuine Christian miracle either.
By framing contemporary miracles this way, when a fellow Christian tells me the things described in the OP, I would NOT dismiss their testimony right away, but discern whether psychology could have been the cause. If psychology is clearly not the cause, then I would examine the fruit. If what happens to the person leads him/her to Christ, all is well.
I do not feel the need to certify whether the one who experiences the miracle is lying, deluded, or crazy. But if a friend / family member starts developing a habit of obsessively seeking miracles to the point of
- excluding "ordinary" means of medical healing (insisting instead for a healing miracle by praying / declaring healing daily "in faith" for months), or
- excluding wisdom & pastoral counsel for discerning God's will (insisting instead on waiting for a vision, prophetic word, or a dream), or
- excluding "normal" prayer to talk to God (feeling "incomplete" without praying in tongue for hours on end), or
- excluding "common sense" way of interpreting an event (insisting instead to automatically frame a seemingly ordinary event as a "God is behind it" event without any discernment, suggesting a post-confirmation bias)
because of several past "miraculous experiences" she had earlier, which she then set as "precedent" and as a "basis" for future expectations, then I would try step in and offer Biblical discernment for the person's well being. (The above description is based on something I witnessed in real life.)
Will my worldview change?
If someone close to me experiences a worldview-changing conversion miracle that is later discerned to be genuine, I would thank God who through the Holy Spirit's activities in the world brings yet another person into the fold. My worldview does not change at all, since it is consistent with what the Holy Spirit is doing in the world until judgment day. This is the time for harvest.
Second hand miracles reported from books like Craig Keener's Miracles Today also do not change my worldview one bit since it is consistent with the Concentric cessationist position.