Hello, Jonathan,
You are going to love visiting George Town and the Grand Cayman. I have wonderful memories of the beautiful scenery of that lovely island paradise from our visit during a Panama Canal cruise aboard the Disney Magic.
I'll start with my opinion that your plan is fairly likely going to work out just fine. That said, several factors could come into play. So I can't say for certain what to expect during your visit to the Grand Cayman. On some cruises I've sailed with my family, I have observed that Guests with Port Adventures booked through the Disney Cruise Line may have priority access to the first few tender boats to accommodate their scheduled times. The timing of your ship's arrival to the Grand Cayman may also be affected by unexpected weather or other unplanned events. The number of Guests who have booked the available Port Adventures may also impact logistics. Fortunately, it appears that the Disney Treasure is currently the only cruise ship scheduled to visit the Cayman Port on the day you will be stopping there. With that exclusivity, I'd assume that your tour operator would be willing to accommodate slight schedule shifts for you and other Guests who may happen to join you from the ship.
Your excursion is early during the time that the Disney Treasure will be George Town. Nevertheless, your question reminds me of my family's experience there. We were booked on the latest available Nautilus Undersea Tour of the day. We had a lovely time peering through the large windows to watch sea life and sunken vessels. Our tour guides were amazing at helping us to have a safe, memorable, and relaxed experience. As the tour shuttle took us back to the tender dock, we learned that we were taking the last tender boat back to the Magic. As we boarded the ship, we noticed that the crew members were counting backwards as each passenger passed through the security station. "Six, five, four, three, two…" When I passed through and scanned my DisneyBand+, they called out, "One!" I was surprised and honored to be the very last passenger to be reboarded from visits to the island. The crew was also very pleased that everyone was accounted for and nobody would be left behind on the island. But we weren't at all concerned about making it back to the ship on time. Knowing that the tour operator and the Disney Cruise Line were coordinating the timing of everything gave us peace of mind. Again, it's my unofficial opinion that your plans are pretty likely to work out OK. However, my personal experience is a big reason why we happen to prefer to book Port Adventures through Disney Cruise Line and I recommend the same to others.
Tony's Tip: As you are enjoying your time on the Treasure, you may decide that you will want to enjoy another Disney Cruise Line vacation soon. In my opinion, the best way to proceed with that plan is to make a discounted placeholder booking using the Disney Cruise Line Navigator app. I know that is exactly what I plan to do while I'm on board the Treasure later this year!
I hope you have a wonderful cruise, Jonathan!
~Tony