First, double check you don't have Input Quantize enabled. I think it's on by default sometimes, and it's not really the greatest default choice for most people.
Then, you might want to check out this post:
First of all, since you said most people must "copy/paste", no I play in my parts same as you.
I would not bother to read most of the discussion and skip to the post I linked because so far, the only things that have been consistently measured and demonstrated related to your issue are:
1 - Monitored virtual instruments have some measurable deviation in latency on macOS only. When I say measurable, I mean greater than ~1ms total.
2. The amount of deviation gets bigger with bigger buffer sizes. I only monitor at 64 so I honestly never noticed it until I helped a user do some tests.
3 - The amount of deviation is only audible at a block size >= 256 samples, whether or not you are using Green Z monitoring doesn't seem to affect when it becomes audible.
4 - The amount of deviation gets pretty bad around 512 samples and above. For whatever reason, some users monitor at pretty high block sizes.
If you're on Windows 10 and experiencing weird issues in your monitored audio then the post above probably does not apply to you and honestly it's probably something other than Studio One that is the issue.