We are just back from Cozumel, Costa Maya and Grand Cayman. We took Celebrity excursions in each port and were among the last passengers to return. Of course, celebrity guaranteed to wait for you if you take their tours. On one tour, we were 15 minutes past departure time. NoDocking in Cozumel is safe but you probably could only visit Tulum as Chichen Itza is a long drive away. Good past advice on Jamaica, stick to boat excursions ans don't wander away.
Problems. We went to Chichen Itza. It is a very long trip for 1.25 hours at the site. Lunch on the bus. Excellent guide with a long lecture with iPads on the way there. If the cruise line sells that tour, take it. Do not take a private tour to Chichen Itza while on a day stop on a cruise. I found the hawking of goods at the site annoying but it is typical of Mexican tourist sites. .