Yeah, its possible that he never actually pushed the culture away, but where do you get 6 culture/sec?  To my understanding, each shot delivers '50' culture.  So 2 shots, means '100' culture, therefore the capital would've had to have more than 5 culture towers (5*20), or maybe an Advent starbase with 3 culture upgrades (3*35), to stop the gun from overwhelming culture there.

Do you have a saved game, or an autorecord, or maybe an autosave before this incidence?  That you can review to see how much culture he had at his homeworld?

Please send in any evidence of a bug that you have.  I've seen passing references to culture being bugged (not disappearing properly), but no hard evidence yet. 

It's fully possible for an AI player to have enough broadcast centers around to completely nullify the deliverance engine. If they have no need to place another lab or trade port they freaking spam them on their planets. Seen desert planets with 8 or 9 of them, so if there were such "cultural hubs" on the planets next to the world you bombarded there is nothing the delivarence can do about it.

I'm just parroting what it says on the wiki "A single deliverance signal will cause a -3 culture rate for the planet until the planet revolts or your culture is pushed away, two blasts will cause a rate of -7 but that is the maximum possible loss"

https://www.sinsofasolarempire.wikia.com/wiki/Deliverance_Engine

People...STOP USING THE WIKI!  It is soooo rift with error....

In part because you can just look at the game files themselves...