All the automatic time zone adjustments happened automatically and correctly with the spring DST changes in the rest of Mexico with my devices accurately setting themselves to "Cancún" time and the "Cancún" settings accurately being UTC-5 year-round. If you have any doubt, Bogota matches Cozumel's time year-round.
I strongly believe it's a mistake to think of any part of Mexico as being "on" any US time zone. Some of them match up pretty well, but time zones are literally like political borders, and different localities observe different DST dates (or none). People who spend most of their time in one time zone naturally want to understand one they're visiting in terms of what they're used to and to set their watches, but there are gotchas sprinkled through the year. The easiest thing is to listen to "welcome to Cozumel, where the local times is..." on landing, and set your watch accordingly if it's not one that reads time from elsewhere. If you have a watch that does set itself (phones, laptops, smartwatches, etc), the easiest thing is to compare what it says to what the flight attendant says in the "local time" announcement. If they match, you don't have to do anything. If they don't (and you're connected either to wifi or to the cellular network), you need to select a time zone. Whatever you do, do not choose any US time zone. Pick Cancún if that's a choice, or Bogotá if it's not.
This is neither difficult not time-consuming. By the time the plane had taxied to a stop, my iPhone, Apple Watch, and dive computer were all showing the local time. My MacBook and iPad showed the local time when I turned them one at the house and they connected to wifi. The only thing I had to do manually was switch the Local and Travel times on my dive computer, which takes 2 button presses. A mechanical dive watch might take 5 seconds to adjust.
To find how you need to change a watch when you go to Cozumel, found out the offset between your current time and UTC. Knowing that Cozumel's is UTC-5 year-round should make it very easy to figure out how to adjust your watch if you want to do it before you arrive on the island and someone tells you local time.