Update:

The hints regarding a button stuck was the correct one!

What was wrong:

The VIRPIL Constellation Alpha has a 4-Step-Trigger (!), means a lever switched forward (button 1), switched backward with contact to the trigger (Button 2), then the trigger itself (Button 3) and a second step on the trigger (Button 4).
If this lever is forward, it sets button 1 to "down" --> Means its pushed all the time --> Means, when i want the game to recognize an axis, the button permanently sends data and the game does not "see" the axis im moving...
When i bring everything in the standard position and all the buttons are shown as "up" - then it works.
So basically my fault with the buttons on my Joystick. Cant blame the game for it!