There appear to be two schools of thought. One uses pure finger power and the other employs some sort of wrist help. The former takes a longer time to develop but I think the musical effect is better. Let's face it, for double note trills between adjacent fingers you can't use wrist anyway.
My suggestion is never to strain, keep light and flexible with full finger strokes without pushing down to the keybed. Aim for a musical effect, not speed, otherwise you might as well play a typewriter. Try to incorporate your trills into some creative improvisation because this willl make you relax more. Don't allow one particular aspect of technique to dominate.