I think your breaker is faulty in some strange way or not properly installed.
The Installation Instructions says that after pressing the red test button:
The DFCI breaker is functioning properly when:
1. The circuit is interrupted.
2. The handle moves to the tripped center position (G) as shown in Fig. 1.
and this is clearly not happening in your case.
The LEDs are supposed to indicate the last fault condition - so my guess is that blinky LEDs are telling you the test button isn't producing the expected result.
Do you have the breaker's neutral pigtail wire properly connected in your panel?
A disconnected neutral pigtail is the only condition listed in the instructions which would be expected to produce a result where the breaker doesn't trip when pressing the test button.
If it's installed correctly but still misbehaving then I wouldn't trust it in my panel ...