as mentioned earlier, Tamiya tape I find to be the best. When I ran out of it last time, I picked some off-brand stuff at Hobby Lobby and it just does not perform as well. It tends to have "fuzzier" edges when cutting and sometimes bleeds through.

However, I do find even Tamiya's tape can bleed through when painting on with a brush vs using an airbrush or spray can. It think it depends on how wet the paint is when it hits the tape, how well the tape has been burnished down and how clean the part was for the tape to stick to

The longer the paint stays wet, and the wetter it is, the better chance it is going to run, especially if the tape does not have good adhesion in areas. This typically happens with clear parts as they are harder to stick to and they also tend to be curved and rounded  that can leave microscopic creases in some areas

I typically get much less bleed with spray cans or airbrush because the paint dries very quickly and is usually applied in very thin layers leaving less chance for it to get under the tape. If you spray too much on though in heavy coats, I have gotten bleed that way as well

For painting with a brush instead of spray cans or airbrush, besides cleaning the surfaces, and burnishing as best you can, I would say to try to apply the first layer or so near the tape as light/thin as you can. I don't mean thin as in thinning the paint, but thin as in as little paint as possible. i.e. don't try to do one heavy layer vs sever thinner ones. And try starting from the tape area and brush into the uncovered model area rather than brushing towards the tape.

Not full proof, but it does lessen chances I find

another option I keep meaning to explore is painting or spraying a clear varnish first, then painting the color after it dries hoping that might seal things, and even if it does bleed, it is just clear?