If ROFR was followed, it is over once the new deed is issued. If the sale went through a closing company, the closing company would not have even gone through with the closing absent a waiver of ROFR.
You seem to have an incorrect sequence of usual events, which actually are:
1. Prior owner and buyer agree to a contract for sale.
2. It is that contract (not the new deed) that must be provided to DVD at least 30 days before the date of closing. If it is a gift transfer, DVD still needs to be notified for ROFR which, if it is a gift, it will waive. However, with a gift there is usually no broker involved and thus the parties involved, particularly the gift-giving owner must provide the notice.
3. DVD then has up until just before closing to exercise ROFR or waive it (and for a gift it will waive it absent a belief there might be fraud in that there is really a sale going on). In the interim there will also be a title search if title insurance is being purchased. The title search will show clear title (most likely) with the exception of not yet having the waiver of ROFR which must occur for the title policy to be issued at time of closing.
3. Once ROFR is waived, the closing goes forward and it is at time of closing that a new deed is issued and sent to the comptroller's office for recording. If you are going through a title company that knows what it is doing, it won't close that sale absent the waiver of ROFR.
4. The new deed (and other closing information showing the purchasers address and phone) is then provided to DVD after closing so the new owner can be added to the
DVC system. If it is a gift transfer, the gifdt-giver or the new owner may need to provide Disney with that info (it is usually something the broker sends when there is a sale but when there is no broker, such as would usually be the case with a gift transfer, the title company may also do it upon request).