The gist is that 3 things constitute a "scriptural" divorce with the freedom to remarry: (1) adultery, (2) a legal divorce, and (3) rejection by the "innocent" mate. One of the things that establishes this rejection is the "innocent" mate's signing of the divorce papers.
They do include a blurb that in some lands it might be possible to sign documents establishing child custody and support but still not consenting to the divorce. I've never heard of this in actual practice, and only a fool would agree to the obligations of a settlement without the freedoms of a divorce.
Anyway, once such a "scriptural" divorce occurs, remarriage by either party is considered scriptural, legal, and binding. Therefore, it would not be considered an adulterous marriage.
That said, the adultery still must be dealt with and the "guilty" mate may not be considered "exemplary" for a long time, even if not disfellowshipped or after being reinstated. He or she would not qualify for any congregation "privileges" till they have "lived down" their guilt and shame. Big whoop.