Does anyone experienced such problems with robotic-ish characters? I dont understand why program doesnt seem like to see the fingers. I did tried different joint placements, they all showed such result.

AccuRig does not deal well with mesh containing sparse elements such as robotic fingers.
Aside from that, to achieve convincing fingers animation each element must be weighted 100% to the respective bone.
Current "Adjust Bone" routine is broken for Humanoids and correct Weight Painting of sparse fingers elements is nearly impossible in CC.
Best advise is to rebuild weights and bones position in 3-rd party app such as Blender.

You may download a free edition of my Robotic Arms to see how it was done: https://marketplace.reallusion.com/robotic-arms

Otherwise you can view how it was weighted to be a solid metal for the most parts:

Yes, I figured that I can weight it by myself. But that still takes a lot of time due to a lot of "details" on the model, and AccuRig already made his own wrong weights, so it just jumping, erasing, painting your own weights. Kinda still sad that ActorCore cant weight robotic parts, which seems somewhat easier than human character.