Actually, I'm pretty sure that's correct. The alarm call (and the bell) was a signal for the crew to prepare for a crash dive (evacuate the conning tower, stand ready to switch to electric engines and stop the Diesels, all crew ordered forward to assist the boat in diving, etc..) while the actual command "Fluten" was only given once the conning tower hatch was closed.
"...late afternoon the Air Tasking Order came in [and] we found the A-10 part and we said, "We are going where!? We are doing what!?"
Capt. Todd Sheehy, Hog pilot, on receiving orders during Operation Desert Storm