If you are moving anything, you are adding tension to accomplish something that isn't working normally.
Tension allows for compensation, so to figure out what is going on, you need to review:
1) breathing practices-are you REALLY getting that big relaxed breath?
2) is your tuning slide far enough in? Many players tune a bit flat to be able to lip up and thus compensate for a weak embouchure or bad horn/mouthpiece combination. This can be easily handled by getting a better routine and a big breath!