The short answer is, “not exactly,” and they are probably not culpable for their sexual relations. In fact, to the degree that each party thinks he is fulfilling his marital obligation to the other, such acts, far from being sinful, would actually be meritorious.
The first observation to be made is that the text from the Diocese of Oakland, it seems to me, needs some clarification. A declaration of nullity (the term “annulment” is never used in Church legal jargon) makes no judgment regarding the sincerity of the parties involved. The marriage tribunal simply analyzes the relationship in question and asks, “Is this relationship a marriage?” If the answer is “yes,” then it is declared “valid;” if the answer is “no,” then it is declared “null” (invalid).
So, in fact, a declaration of nullity affirms that no marriage existed between the parties, or, if you prefer, that the conditions for a marriage were never in place.
As regards the O.P.’s question, as Geremia pointed out, sexual relations between two persons who are not married is called fornication not adultery:
Fornication is carnal union between an unmarried man and an unmarried woman (Catechism of the Catholic Church [CCC] 2353).
On the other hand,
Adultery refers to marital infidelity. When two partners, of whom at least one is married to another party, have sexual relations—even transient ones—they commit adultery (CCC 2380).
However, before coming away with the idea that couples in a putative (but invalid) marriage are living in sin, it is important to recall that couples in a putative marriage usually believe sincerely that they are married while that putative marriage lasts. In that case, they are not (to use the terminology from moral theology) formally committing acts of fornication. In other words, they are not guilty of any personal sin for the mere fact of having sexual relations.* Indeed, since each party probably believes that he is fulfilling his marital obligation to the other (and to the degree the each one is convinced of that), the actions would actually be meritorious.
(It should be noted that one of the possible grounds for a declaration of nullity is the existence of a previous marriage, kept secret from the other party. In that case, the sexual relations would, objectively speaking, be a kind of adultery. Naturally, the degree of culpability would depend on the knowledge and deliberateness with which each party acted.)
* According to Catholic moral theology, three conditions must be fulfilled in order for a person to commit a grave (mortal) sin: (1) the action itself must be gravely immoral, (2) the person must know fully what he is doing, and (3) the person must give full consent of the will (he must be not be motivated by grave fear). Regarding condition (2), the lack of knowledge can be about the particulars of the situation (e.g., when a soldier mistakes a fellow soldier for an enemy and accidentally shoots him), or else about the norm itself (e.g., many Catholics are not aware that contraception is gravely immoral). See CCC 1857. In the case of a putative but invalid marriage, there is clearly a lack of knowledge of the particulars of the situation, even though, objectively speaking, any sexual act would be a kind of fornication (or adultery in a few cases). In such a case, the sexual act would not even entail venial sin (and, to the degree that each spouse thought he was fulfilling his duty to the other, would even be meritorious).
