I actually use this technique on the "inside of the window in the kitchen" right after my first try on on the base and door casing that I let set too long. It really did a nice job, that said I doubt I use it for anything beside something like that but for trim against a wall I'll just use the typical finger swipe as I don't think it's worth the time to tape it all off IMO and YMMV.
Ok, Im confused. Are you caulking to fill cracks, or are you just trying to make a perfect tape line for paint? Cuz its two seperate processes, (usually)
If you are painting a wall and a jamb, you would calk the jamb to the wall, paint one or the other, then, if so desired, run tape and caulk for your perfect line. If you need to keep caulk and paint off the other surface, like a cabinet, or window, or whatever, you could use the tape method to kill two birds with one stone. Tape, caulk, paint, pull, while its wet. Theres still a technique involved though. it has to be taped a certain way. If the tape is too close to the corner, it will mess up the caulking when being pulled. about a 1/16" out is usually good. You still need to wipe as much as you can off the tape edge too.
Also, what video did you watch? Some of them have unnecessary steps. For example, if you are going to caulk over your tape, theres no reason to use expensive frogtape, or even blue tape, unless the surface itself is delicate. Regular old masking tape will work. if you're using frogtape, and the wall isnt textured, you can dampen the edge with a wet rag, and that seals the tape from bleed through, so you dont need to caulk it. It doesnt always work as well though.... Using frogtape and caulk is a waste of money.