You stop worrying about it. Seriously, it will fix itself over time. The reason why you are making a mistake with your thumb is because you have not developed the coordination(the hundred plus muscles involved + the neural activity) to give you precise control. The same is true for anything/everything as everything we humans do is mind/body.
Over time you will develop the conditioning, coordination, and precision if you just play a lot. Yes, you can target train things when you feel it has become a hindrance.
Generally speaking though a lot of faults are not due to what we think they are and so when we target something we are actually wasting time since we are not targeting what we think we should. This is why most teachers are very bad. They might tell you, spend 3 hours moving your thumb at 3bpm from one string to the other. Sure, after a few weeks you will be better, maybe reduced it from 5% to 4%. Was it the best way to go about it? Did it really solve the "problem" or just solve some "problem"?
The more you play and the more you try to be aware of all the elements(be in the moment rather than thinking about what you will do once you get done practicing) the more everything comes together.
Learning and skill work on the pyramid principle. The base is very large. That is the rudimentary things you must learn(a lot of stuff and hence the analogy with a "big base") and then there is layer after layer but they get smaller(like a pyramid made out of blocks) after some time you are near the top and things get easier and easier. Yes, some people seem to get very good in 3 months. They build very small pyramids. Sure they are very good at very specific things which is all they do and all they show people but they are terrible at everything else. Oh, it's impressive but it is not very fulfilling and they rarely learn to build a big pyramid because they get stuck showing off their shiny small one to people to get attention. These people are like the hair who run as fast as they can but then run out of energy before the finish line. They want to cross the line so fast so they can sit around and do nothing but get the accolades from winning. Then there are the tortoises that just go steady and slow knowing that one day they will cross the line and it really doesn't matter when. If they "win" they "win" but that isn't their problem because they are not racing.
What I'm talking about here is that you should take the "big picture" and "long term" approach. Just learn as much as you can about everything and do as much as you can(don't waste time on useless things like watching Southpark or masturbating).
The number one "trick" I used to go from peon to master was this: How does a master think? See, the issue is that you think like someone who has problems and so you have them because you are them. If you want to be different(someone without problems) you have to think different(but you don't know what because you aren't a master yet).
The different between a peon and a master is that a peon/student/etc seeks out gurus/teachers/masters/etc while a master looks inside to himself for the answers. This doesn't mean a master never learns from anyone else but his approach to overcoming his obstacles is to use his own mind to find the way around them.
No one on the outside can give you the right answer because the right answer depends on context, a context which they actually don't know. They assume it must be the same as their context(their experiences, issues, beliefs, etc) but it usually is different enough that their "answers" are not very effective.
A master, if he had an issue with something, would sit down and solve that issue. He would figure it out. Bach, for example, didn't have the internet and didn't have master teachers(although he did have masters around him) to tell him how to do it all.... he simply did it himself.
So my suggestion is that if you think it is a problem(and only you know if it is a real problem) then what would a master do about it? Would he go play call of duty? Would he pick his nose? Would he read Poe? What would the master that you want to be actually do about the problem? Would he learn new pieces? Play very slow and work up to tempo? Would he target that specific issue? Would he study sight reading? What would he do?
See, you have to come up with your own approach to solving the problem and in a way where it is actually you doing it(that is becoming the master, it is a process and the more you work on it the more effective you become at it). E.g., you asked for a general solution and that is what I've giving you. The general solution is for you to figure out how to solve these types of problems yourself so that you can solve those types of problems yourself quicker. If you always look for external solutions you will always look for external solutions and they generally take far longer than internal ones.
One of the things that has helped me but may or may not help you is that if I feel like I need to perfect something then I just do it. If it's not as good as I want I do it until it is. Some time that doing may be a minute, an hour, or several "sessions" or nothing at all. Just all depends. A "master" doesn't go by a fixed set of preconceived rules about how to do things, a master handles each second as it comes and tries to make the best move he can. As he does this over time he gets better at making better moves.
When I was first learning I would look externally for all the answers I watched thousands of videos and I tried to do as people said... nothing worked well. Sure I made progress but I always felt like there was some missing piece of the puzzle. One say I said "I'm going to sit down and figure this shit out on my own and I'm not going to stop until I do"... and so I did. It turned out that it was like everything else I figured out except it took me a long time to realize that is all I had to do.
Do you understand?