Homestead Exemption question

[Huy Thai]

PROPERTY TAX QUESTION: If I'm buying a home that has homestead exemption with two months left in the year as an investment property, do I get to benefit from the homestead discount for the 2 months that I'm paying for 2019? Seller contribution for 10 months is based on the discounted amount with exemption. What I don't want is for the tax man to come asking for the full amount (non exempt) come Jan 1 which would mean I'd have to fork up an additional $600 for months that I didn't own the home. 

I guess my question simplified is once it's designated, does the Homestead last the whole year even if the property changes hands?