Sanguina starts each room with 6 purple balls circling her.
The polymorph effect is triggered when an enemy shot comes close to one of the balls (there is probably a random element to it but it’s hard to figure out the chances)
Once triggered, after a short delay the vampire attacks an enemy and causes damage equal to 20% of Loadout attack. This can be seen clearly in this clip where the attacked enemy isn’t receiving shot damage:
Sanguina’s loadout attack was 4449, of which 20% is 889.8, which rounds down to 889.
And in this video we can see that the damage extends not only to the enemy attacked by the vampire, but also nearby enemies (look for the 889 that appears in the frozen segments). Also, as the 6th vampire is proc’ed, another purple ball is generated - presumably this is a coincidence, as we don’t have another being generated when the 7th one procs.