Closing plus 3 days is not uncommon and can be for a number of reasons, moving is the most common. Recording of the deed typically happens on closing.
I would want to know that the seller's are packing and lined up for their next home. If all indications point that way, I wouldn't panic. If this is a short sale you may have a concern and want to discuss changing the terms to vacate prior to closing. Distressed sellers have often been living rent/mortgage free for a number of months. There is no reason they need to wait for the home to close to move out.
In the case of a conventional seller, they may be waiting for the proceeds of the sale to close on their next purchase. Most sellers will not allow someone to move in prior to closing, so they wait until both sales are closed and then move. If they need the proceeds to purchase the next home, then asking escrow to hold them would aggravate the problem, not solve it.
Have your agent investigate the sellerâ€™s plans and make certain they are preparing the home to move out.
if escrow has not been closed then don't wire the money, don't sign any thing ...