A few of the houses I have been selling have been rehabbed. They were purchased as inexpensive fixer uppers. Sometimes the sellers are able to get a lot more for the home than they paid for it which is kind of the idea.
Some of the lenders don’t like to see a huge increase in value in a short period of time so they have the home appraised twice. Honestly I think that is a good thing but it can slow the process, and I think they go with the lowest appraisal if the two appraisals don’t agree.
Most home buyers need to borrow money to buy a home and it is the lender who orders the appraisal. The buyers and sellers do not get to choose the appraiser.
What happens if the appraisal comes in lower than the amount the buyer and seller agreed upon? Sometimes a lower price can be negotiated. I have never heard of a buyer kicking in some money of their own and the lender going along with it, but that could happen. Often the sale falls apart. I have sold houses twice and had them appraise the second time around.
Be prepared for two appraisals. Don’t do the happy dance on your purchase or a home or sale of your home until the appraisal comes back.