Generally speaking it does not take 15 days for an appraisal to be done. Likely the required pre-appraisal events did not happen in a timely fashion. Once you're lender has received an executed (signed) purchase agreement, your lender can start the process. In any type of lender mediated transaction, it may take weeks for the fully executed signatures to occur. Most lenders won't risk ordering/paying for the appraisal up front. Some have the buyer pay for it upfront (non-refundable). When that happens... It's usually done in a couple of days... Money talks.. Likely there were still some issues in this agreement with respect to contingencies etc. Best of luck with your purchase.
A few months ago I had an appraiser take 10 business days to get the appraisal to the bank. It was an FHA loan, and the appraiser had to go out to the house a second time because the bank wanted him to look at something. It really upset the buyer and pushed the closing back. Hang in there, the whole process is taking longer for some lenders and homes.