I can only answer this question for my state (KS), so take this for what it's worth.
In KS, January 1 is the date on which the property is valued to determine property taxes for the year (this seems to be consistent with your builder's explanation). However, if a house is partially completed on January 1, the county assessors generally assess the value of the home on a percentage completed basis. So, if the house would have been worth $100,000 on Jan 1 if completed, but is only 50 percent complete, then the value of the improvement (not including land) would be $50,000. It is possible that FL has a statute that does not value the improvement (i.e. the house) until it is complete. I haven't heard of any state valuing properties for property tax purposes that way, but it's possible.