You can have your T/A do it. In fact, they have to do it. RCCL won't do it prior to boarding UNLESS you booked w/them. You can also actually just wait until you are on board and go to the little podium desk where you can make dinner reservations for MyTime dining. (Ask at the purser's desk where this is, but it will also be listed in the daily newsletter when you get onboard.)
We changed our late dinner seating to MyTime, then back again the next day when the MyTime was not turning out to be a very good choice for us. The reason? It was fairly new to the ship we were on this past May in Europe. There was a small quadrant of the middle level dining room (ship had 3 levels) set aside for MyTime dining. We had been told that if we requested to be seated w/others, we would be. However, after a few min. our first night w/JUST parties who wished to be seated together by themselves (mostly young couples or families) and being escorted to their tables w/out being asked if they'd mind having someone sit w/them, we were seated and told that we could have a table for 4 and IF someone else showed up that requested dining companions, they would be seated w/us. Now, that was kind of odd as we had to order, etc. It became clear that it was not the convivial type of "anytime dining" we had experienced on Princess (there way of doing it is different and you tend to find that in general most people show up around the same time each night, often end up being seated w/some of the the same people who come in that time period, and getting the same wait staff! Maybe people hook up in line w/those they had dined w/the night before, though if you ask for a lg. table, there are usually new folks as well. And RCCL's way of doing it is also a bit different from NCL's version of Anytime Dining.) We were told that not enough people knew about it or took advantage of it on RCCL yet, though it was highly publicized. The way it was working out, it wasn't our thing on this line. We ended up sitting w/a 2 other couples from the UK who were not traveling together, plus some honeymooners. The wife nearly went to sleep before getting her first course, and I THINK they probabaly DID switch to Anytime Dining as they were 20 yrs. younger than most of the rest of us -
So my suggestion to you would be. . .choose the seating you want and stick w/it UNTIL you get on the ship and decide then what you want to do. Esp. if you want late seating as that one seems to fill up first. Hope this helps!