I don't use the A/P that much, so hadn't noticed, but yep...I see the same thing. When it initiates a turn, it's like BOOM, it snaps over right away, then slows to a normal roll-in to a turn. Roll-outs are normal. Adjusting the Heading bug or NAV courseline or what have you, and BOOM, does it every time. I messed with the sensitivity a bit, but only just to futz around and see if it affected it, not as part of any tuning procedure. Lowering it to 8 *seemed* to help, at first, but it was still there.
It's like it's got a step function in the entry to the PID loop, going from 0 to the desired angle as quickly as possible on entry into it.