I looked a little and it seems that the actual text of the law just uses the term "own" without explaining what that means.
I think there are several reasonable positions a taxpayer could take:
1. Ask the IRS what to do then follow their guidance. Note that the IRS specifically disclaims that this protects you from further IRS issues - that is to say, it doesn't.
2. Take the position that the majority of the ownership of the home is the owner of the home, since that person or persons is the one who presumably could decide whether to sell the home, and whether or not one can sell something indicates whether someone owns something. Then do the calculations from whenever you became majority owner.
3. Take the position that owners, like owners of a corporation or a partnership, can be minority owners, and do the calculations from whenever you became an owner, even if you were just a minority owner.
4. Take the position that ownership is proportional, so take 25% of the credit for the period of time when you were 25% owner and 100% of the credit for the period of time when you were 100% owner.
5. Pay your CPA to do the research for you and follow their advice.
At the end of the day, the choice probably boils down to how by-the-book you want to be and how aggressive you want to be in your position. I generally take the most aggressive position I can as long as it meets the letter of the tax law and there is a reasonable argument that supports it, but I know others who feel differently. It's your signature at the bottom of the tax return.