Ins_FPS

It's probably  just because they are different games. Every game has a slightly different setup as far as input / processing delay, strafe speed and acceleration plays a huge part, because people very rarely stand exactly still when aiming, the amount of sway or headbob, some use a fixed camera position directly on the pivot point that your character "floats" around, and others mount a camera physically into the character model which affects the pivot point and aiming feel slightly.
Don't get too hung up on trying to get it to feel like EXACTLY like another game, the point is getting it to feel close enough to what you are the most comfortable with, and finding what approach to take for different FOV conversion methods works best for you.

For me (and not only for me) it has to do with the sensitivity, when it's really low you can do it with the wrist with the same accuracy, at least I can. I never felt the need to use the fingers with 55+ cm/360
If we talk about few pixels movements, sure you can help yourself with the fingers in some situations, but that's it, and depends by the grip as well.
If you palm or claw you have a very little space to move the fingers and if the sensitivity is really low, often you won't have enough space for significant microadjustments and you just destabilize your aim if you force the use of your fingers or if you stretch them too much trying to microadjust. That's my experience at least.
Instead when i switched to a higher sens after playing faster games, my grip naturally changed after switching mice and I felt the need to microadjust with fingers cause it was actually really effective and it wasn't hindering my aim in any scenario .
This image shows one of the best CS players not doing microadjustments with fingers like you say. And there are many others.
Remember we all react differently so it's hard to say if something is right or wrong. For me, the game I play, the mice I use and especially the sensitivity, are the factors that determine how should i move the mice.

 

I played CS with 58 cm/360 for a long time, using claw grip and wrist only. The lower the sensitivity the less your fingers are effective.
Right now I play with 40 cm/360 and overall higher sens cause I play faster games and i use wrist and fingers together with a hybrid fingertip grip. It's really hard to master this kind of playstyle so don't force yourself. As i said I used claw for many years and when i switched to a smaller mice and increased my sens it came natural to me.
 

Imagine feeling the need to call something the R word and make a thread out of the inconvenience of having mouse acceleration on for 3 seconds while you login to your PC

Verified this now, no effect yet but at least it seems like it will come at some point.