I have a list of 12 shops that offer afternoon dives, requiring from 2 - 4 divers to go out. (Aldodra is not on that list due to the caveats). PM me if you'd like the list.
I am quite certain there are no ops based in Tulum that will lead dives in Cozumel.
The dive shops in Tulum don't really market ocean dives as the diving, according to them, is mediocre. Their push is cenote diving.
Never done the mainland ocean dives from Tulum, but have dived both PDC and Puerto Aventuras. While not the high adventure drift dives on walls that Cozumel offers, we enjoy all the healthy marine life we see during our diving from Puerto Aventuras. We also dive the cenotes, and they are exciting, as well.