Have never done it myself but if you have the same cabin I think you can stay onboard in some ports (may have to do with custom regulations etc). At least that is what I have heard. Could not find any info about that on RCI website.
I know Christoffer has done this a couple of times (if I'm not wrong both an Oasis and Allure) so he should know.
Done a b2b cruise with the Navigator, Liberty, Oasis and Allure of the Seas.
All I can say, b2b cruises are the best!
You will get a letter to the stateroom during the cruise where to meet on the last day on your first cruise, it usually at a bar or other lounge.
You will get the second weeks room key at the b2b meeting, there are also staff to help you to book shore excursions or table reservations to specialty restaurants, if you have not already done that before the cruise.
When you have the same cabin, there is nothing to worry about.
Had to change cabin only on one b2b cruise, but it was not that bad.
As a b2b passenger, you will be the last passengers to leave the ship after the first week.
You will be escorted to the terminal and the immigration, after this you can go directly back to the ship and enjoy a short moment the ship for yourself with the other b2b passengers.