In addition to consulting through InformedAthlete.com, I previously consulted with college athletic departments on their compliance procedures, including those making the transition from NAIA to NCAA Division II. The transition period lasts 3 years during which the school is considered a "provisional" member of Division II.
Typically, the NAIA school will be barred from NAIA post-season in the season immediately following their formal announcement of transition. The school won't be eligible for NCAA post-season until they become full active members of Division II after the provisional period is completed.
They also must be admitted to a Division II conference before becoming a Division II full active member (i.e., no independent D2 schools). The comment above about travel is a great point as some of these colleges attempt to join suitable conferences. Some schools may be allowed by their conference to play a conference regular season schedule while they are in the provisional stage, but can't participate in the conference post-season tournament until they become a fully active Division II member.
Some church-affiliated colleges join the NCCAA (National Christian College Athletic Association) during the "provisional period" on a temporary basis so the athletes at least have some opportunities for post-season competition and a chance to win a "national championship."