This bug is a direct result of MC-135194

DISCLAIMER: Please ignore the normal piston in the bottom left, it's a completely different bug.

When a sticky piston ejects an observer into another observer, the second observer gives off 2 pulses with How to replicate:

Green button (hard power):
Rising edge: Working as intended, Redstone dust pulses twice
Falling edge: Working as intended, Redstone dust pulses once

Noteblock button (1 tick power):
Rising edge: BUG, Redstone dust pulses twice with a shorter delay between them
Falling edge: Working as intended, Redstone dust pulses once

 

In 1.12.2 and 1.13 the delay between the 2 pulses from each button is the same