I know exactly what you are doing as I have seen it so many times
so don't think you are alone BUT the problem is easy to solve
although I'm not so sure it is easy to explain
so I'll just get started and we'll see what happens!!
When you train your brush to have a flat side (2 actually
) the reason why the hairs twist is because you are twisting the brush as you work from the middle to each side and back again and not keeping the flat side of the brush facing the nail
What you must try to do (and see in your head as I explain) is to keep the flat side of the brush always
facing the part of the nail you are working on and only paddle
straight up and down whilst pressing the product into place. You will need to rotate your brush in your fingers while you work to do this first to the left and then to the right but always keeping the flat side of the brush facing the nail. Then smooth over the whole zone you are working on first 1, then 2 and 1 and then 3,2, and 1..
It's kind of like when you were a child and made sand castles! If you wanted to smooth the top of your castle, you had to paddle straight up and down gently onto the sand. If you twisted your spade and hit it with the side, you dented it or knocked it down.
If this doesn't 'click' with you, then let me know and I'll try to think of another way to explain it that will.
By the way, some people put a mark (maybe a small bead of polish) onto the place where they place their thumb or index finger to act as a reminder of where they hold the brush -- the lettering idea is good too if it works for you.