The Buttons thing is a separate and far less common issue. Your thumb is everything. I've had this happen to me while fielding (analog throwing, and also with the left analog stick while moving my PCI (zone hitting). It's not necessarily your fault, the PS3 analog sticks are weird and snappy, but the root of the problem is that you aren't paying enough attention to what your finger is doing on the stick. Try to physically keep the stick tilted upwards. Don't just let go and then use your thumb as a barrier (ie: continue to guide the stick upwards even after you've flicked it upwards.
I'd bet this happens far more frequently when the pitch comes to a certain side of the plate. Try paying attention to where the pitch is when this happens, you should see a pattern. Try to make sure you are accurately flicking the stick. The smallest tilt or waver will register as a swing before your swing. If you are trying to flick towards 11 o'clock, and your thumb makes even the slightest tilt towards 9 o'clock, that's a swing. Then as you continue moving upwards, the game thinks you are pulling back.
I hope I'm making sense. Again, it's technically the stick's fault, don't think I'm accusing you of anything, this is just the way I've found to avoid it.