We were on the Mariner last week - it holds over 3,000 passengers and was sold out.
The only time we waited for a tender was in Cozumel. I don't know how Princess arranges the tenders, but Royal Caribbean passed out tickets and you boarded your tender when your number was called.
I overheard people who waited until later in the day to get their tender to Cozumel, and they did not have to stand in line. We did stand in line for a few minutes for our ticket, then sat in a lounge for about 30 minutes until our tender was called, but we were going ashore first thing in the morning.
In every port we returned to the ship early --- in time for a late lunch. So not only did we never waited for a return tender, we also got to eat in peace on the ship. I did see huge lines of people waiting to tender back to the ship in the last hour every day.
If you plan your days out to avoid some of the lines, you should be just fine.
Hope you enjoy your cruise!