I am trying to do some hand fingers posses, in Mocap Studio eveything looks fine, but when I export the animation I got wrong finger animations in several softwares (Unity Engine, Blender, 3DS Max)

Does it look all wrong or only partially broken? From you screenshot I have an impression that some joints are confused between fingers - e.g. thumb and index. Probably this is a result of wrong joint mapping.

As I said, I just added the default pose for the both hands in mocap studio (straight fingers), opened it in Unity, selected the rig to humanoid, opened the avatar configurator so you can clearly see the difference. And the same thing for relaxed pose, it looks other way in Unity.

Maybe I am doing something wrong when exporting the animation? I just hit export with default ipi rig and open it in unity.

First to note, Unity actually switches thumb and index joints when creating avatar for default iPi rig automatically. So at least you need to edit the avatar and re-assign XFinger0.. joints to thumb fingers and XFinger1.. joint to index fingers. However, even after that I see some strange angles in those fingers.
I suggest to do motion transfer to your target character inside iPi Mocap Studio and export retargeted animation. In my experience this produces expected result.
We'll check FBX export function for default rig to see if there is some bug there regarding fingers.

Ok thanks, will try that!