This does apply only to tender ports. Those with shore excursions will be gathered to wait, usually in the theatre, and it can be long wait since these people are usually scheduled off first and the ship might not be able to take passengers ashore right away
If you are going ashore on your own, you will go to one of the lounges and collect a tender ticket only when you are ready to go ashore. Then you will wait there until your number is called, usually just a few minutes unless everyone wants off at the same time. But you are asked not to go collect a ticket ahead of time since that just mucks up the whole system if people aren't ready to get on the tender as soon as their number is called.