Ya sorry was all caught up thinking how to explain how to post videos I forgot to post again about your initial question!
Yes, some people I know do it like that, I have done it also. I also know people that just wait for theirs to bud and leave babies behind on the rocks... they are too afraid to take a knife to them and still though in a year get maybe 6 RBTA babies just from budding. So its up to you. I once divided a lot of ricordea and they got infected and wiped out rather fast, so if you do it I would advise perhaps only divide one into two instead of 4 (like the guy showed in the video) your first few times doing it so as to lower the amount of surface area any deadly bacteria could take hold onto. A UV or Ozone running on the system where you would be holding them would probably be beneficial to keep down the amount of water borne bacteria and such that could infect the animal after your cutting. I have some rock anemonies here that I do this to all the time though and that system has no UV or Ozone and I've never had a problem. So theres different ways to do it and different levels of risk you can take, between how many times to cut the animal, to the equipment on the system, to what you do with the animal once its cut (place it in a container where the flow is gentle is a good idea so it can heal and take hold without being blown around the tank). Hope the info helps. I say give it a try, yes its safe, just some things to keep in mind to keep it even safer.