If the iPad has been fully shut-down, by design the iPad will automatically restart when connected to its Power Adapter or other source of external USB power.
You can, however, shut-down a running iPad - after connecting a power source - while it continues to charge. The iPad will remain shut-down unless charging power is interrupted - at which time, when charging is restored, the iPad will again restart.
If your iPad cannot be shut-down during charging, this would indeed be abnormal behaviour.
I hope this clarification of expected behaviour is helpful in understanding precisely how your iPad should behave while charging.