That same frame roll/tip on a trike causes the right wheel to leave the ground. In order to counter act that, and essentially prevent the frame from rolling/tipping at all in the turn, is to move your weight to the right so that wheel stays grounded.

If you really push and try you can get the left wheel up on a left turn but it’s more effort than popping a wheelie on a two wheel bike. It’s hard to do on accident.

I would guess it has to do with the direction of force changing, the left and rear tires getting closer and the right and rear tire distance getting farther and what that implies regarding the distance each wheel needs to travel in the turn.

Edit: maybe tilt is a better word than roll and tip, basically putting the frame less upright is what I mean by that