There are 2 things that I've experienced that cause issues with the pitch changing when you lock the string clamp at the nut:
- The string retainer is too high. It should be low enough that it pulls the strings all the way down in the backside of the nut slots
- The lock block "twists" when tightening it. Some of them are too small (in my opinion) and allow enough space for the block to rotate. Typically I've only had issues with the E and A strings. And usually the lower string goes sharp and the higher string goes flat. That's because the block rotates clockwise which pulls the lower string towards the headstock while pushing the higher string towards the body.
To solve #1, you can simply lower the retainer bar...
To solve #2, I find that tightening with fingers first helps. Alternatively, if you manually "pre-rotate" the lock block before tightening then it can't move further.
@Andy Eagle - thoughts?