After half a dozen failed attempts against Traumadriver (E6) I have concluded that Purification Drone is not jumping to other group members with Lifeburn.
If you DefTarget someone with lifeburn and use the gadget it will cleanse, which, hurray, however if you use it on someone without lifeburn while another group member is afflicted, it will not jump to them.
Inconclusive if it will jump between lifeburn afflictions if the targeted person has it first. - Edit, confirmed (against Machine Tyrant), it does not.