Indeed, there is more than one way to do it, it all depends on what you find most comfortable.
I just roll the 120 film off the spool and into my hand (keeping in in a roll of course). I remove the tape when I come to it, so the film is free to adjust itself as-needed. Then I roll it onto a 620 spool and when I arrive back at the beginning I re-attach the tape. The concern exists of course that the film might shift out of position fore or aft, but I have not seen that to be the case.