Thanks for the update and I have now further investigated the changes and the 300 ms input lag is gone in active mode as suspected. Very appreciated! The reaction times are now more or less correct when compared to other applications. Maybe still a little slower in measuring reaction times using these buttons together with the Unity Engine. It's however hard to say where the bottleneck is, if it is in the button detecting and sending the presses to the Android OS, or in Unity Engine detecting the press events etc.
Thank you for the feedback provided in this tread.
Have a nice day!