In one run I had a Speaker, a Mirroring Flagbearer, and a Supplicant whose ability was randomized by Birthing stone into "In combat, whenever an adjacent follower gains stats, this follower will gain the same amount." But when the Flagbearer copy was summoned, only it received the bonus stats from Speaker--the Supplicant's stats remained unchanged.
In another run, I had a Sculptor implanted with the Mirroring aspect, but the clone's start-of-battle ability would not consistently trigger; it only happened around 20% of the time (depths 40, 44, 46, and 49 had the clone Scultpor produce no statues; depth 42 had the clone sculptor produce statues).
In another run, I used a Rebirthing Stone on Obelisk & its ability remained the same.