In all my Cozumel trips and plenty of dives, I've never been on the surface more than 5 minutes, and never heard personally from another diver who waited more than 10 for their boat. Being left for almost an hour is definitely not a regular occurrence in Cozumel, no matter which dive operator you go with.
Communication... in this day and age of the internet, texting, cell phones, etc., etc., I think a lot of us have come to expect instant response to every contact we make anywhere for anything, and for some people, if they don't get it, they see that as poor communication. I don't think waiting a day or two to hear back from someone is unreasonable, especially when you're dealing with a small business that doesn't have a dedicated admin or customer service person.
If I had been left for almost an hour after a dive, and it was my first experience with a shop, yup, I'd be pretty upset and angry about it. If I didn't have the owner (or in some cases at least the manager, if there is one), make contact with me within 24 hrs to acknowledge what happened and hear what they were going to do to compensate me, I'd be contacting them. Signing up on a forum and using my first post to slam them publicly, that would not be how I would approach the situation, but to each their own. Maybe as a very last resort if I exhausted all my options.
Kudos to the divemaster for doing a great job and keeping everyone together, calm and safe. Kudos to the shop for refunding you immediately after hearing what happened from their staff, and for trying to make contact with you. I don't know where you were staying but it sounds like leaving a message at the desk wasn't an option?
If this was my first Cozumel diving experience, it would probably be awhile, if at all, before I went back again. I've had a couple pretty crappy experiences elsewhere and they are places I liked enough that I will go back, but I'll use a different dive shop. With diving, if you do it enough, eventually you will have gear problems and a few less than stellar experiences. I hope the new diver in your group enjoyed the diving enough to get past the experience that happened after the dive and not be scared off. Glad it all ended well, everyone made it back safe and sound, and hopefully you went on to enjoy the rest of your stay in Cozumel.