Low E Axis Goes Sharp

The low e on my Axis goes sharp when I depress the tremolo bar. When I bend the string after it goes sharp it goes back into tune. The other strings are not affected so it seems it’s not the bridge. It is level and decked. I tried clamping the strings at the first fret just to make sure there is not some kind of issue with the locking nut allowing it to slip and shorten. If I hold the bridge completely down so when I bend the string it doesn’t move and the tuning still corrects itself. I changed the string to see if that was it but no change. I can’t figure it out. Just seeing if anyone has any ideas as to where the problem is.