WHen the dilverance engine hits... it acts like you just placed like 5 culture centers on that planet.... after your culture neutalized the enemy culture, on that planet, it spreads to adjacent planets... and continues untill the effect wears off... at which point, the culture begins to retreat.
fireing multiple engines at the same time MORE THAN DOUBLES the effect... 3 engines raise the culture rate to rediculous. 4, of course, to ludicrous speed... after 4 doesnt seem to effect anymore... IIRC... but while the effect will be crazy... it will wear off in the same amount of time.
staggering your deliverance engines causes the effect to last longer, and so the enemy culture does not have time to recover.
the dilverance engine also gives you ships a damage bonus... and unless the enemy has a zillion broadcast centers, will also give you your shield mitigation bonus.
I hope that answers your question.
remember... all it is like placing multiple temperary temples of communion on the enemy planet... (+dmg bonus)... so it will act as if you placed multiple temperary temples of communion on the enemy planet... that is all it does... and as such... it is limited by the max -allegance change... it will take a nice little while of staggered deliverance engines to flip a planet... but most important bit of it is... is to give you your culture bonus, and a damage bonus... because... a+10% shield mitigation bonus on a level 10 advent cap ship + guardians + shield restore is very very close to invincible.