They take whoever's elite they're spec'd most into - I took random heroes and henches outside with Odgen using mimicry. The first elite he took was Mhenlo's WoH. I took mhenlo out, and he then took Healer's boon from Tahlkora. Then i tried setting his Prot prayers to 12 and everything else to 0, and he took Lina's ZB. Finally, I set his attributes to 0 and went outside....he didn't use Mimicry. I slowly highered his prot prayers and when it hit 7, he took Lina's ZB.
That mean's you pretty much have control over what elite heroes will mimicry. You can have a monk hero take Healer's boon off someone, and with really high Divine favor and an enchanting weapon, it'll have about 20secs of downtime. During the time it's up, WoH heals for 195hp at 15healing, and 345 when you get the conditional healing


They use mimicry everytime it's available so you don't have to micro anything.