Hmm, I've never heard the term "Cessationist" before, but the description in that article petty much matches the beliefs of many churches that I've attended.
Anyway, most non-charismatic evangelicals that I've known -- fine, I'll call them "Cessationists" -- say that a person is "filled with the Spirit" at the moment that they accept Christ. "Salvation" and "being filled with the Spirit" are seen as either simultaneous events or two names for the same event. Charismatics will normally say that they are two distinct events. A person can be saved but not be filled with the Spirit until a later date.
Also note that charismatics normally say that when one is filled with the Spirit this immediately results in speaking in tongues, and that if you do not speak in tongues you are, ipso facto, not filled with the Spirit. Cessationists say that speaking in tongues is only one of many spiritual gifts, and one that is no longer given to believers. Cessationists distinguish the "sign gifts" of tongues and prophecy from the other spiritual gifts mentioned in 1 Cor 12, etc, like teaching and administration. They then say that we no longer have apostles, as Christ is no longer here to commission them, and we no longer have sign gifts, as they are not necessary.
The verse most often cited for this is 1 Cor 13:8-10
Love never fails. But whether there are prophecies, they will fail; whether there are tongues, they will cease; whether there is knowledge, it will vanish away. For we know in part and we prophesy in part. But when that which is perfect has come, then that which is in part will be done away.
They then explain that "the perfect" is the New Testament canon: Now that we have the New Testament, we no longer need these sign gifts.