I had that too, it is because the faces have different values of color, so the engine makes them move differently.
To avoid that, make sure that in Blender you separate the leaf you want to paint, then make sure your brush hits all vertex at the same time and then paint with 100% intensity, to make sure all the vertex receive the exact same amount of painting.
To still have variation I set the brush strength to 0.1 or so, so by clicking the mouse multiple times I can calculate exactly how much paint will be added, like click 5 times, will make it 0.5 on all surfaces equally.
To do the paint properly I paint all leaves individually and then assemble them into the foliage model, or you paint a branch once and then dublicate it, to save yourself time painting every one. You can add a different shade of green to each one using my previously explained method so each moves in different frequency.
Alternatively you can just select all leaves and set them to color blue through the menu without using the brush, that way you can be sure everything is equally blue.
The most simple method is to set the whole tree, plant whatever to white aka all colors and the stem to black, so it will not move.