As long as you see "AT&T", "Verizon", or whatever carrier you use on your screen by your signal bars you are using your personal plan, whether at the pier or underway. If the screen says "Cellular At Sea" or some other unrecognizable name or number (usually in a XX-XXX format) you are roaming.
The other week while on Oasis my son had a good AT&T signal up to about an hour after we left Port Everglades before his phone dropped it and switched to the Cellular At Sea signal.
If you use AT&T they have some plans you can buy specifically for Royal Caribbean, which give you X talk, X texts, and/or X amount of data. These kick in when using the ship's signal.