The igniters A and B alternate exactly like you say.
As far as FADEC, the FCOM does not differentiate between FADEC A or B. They say there's FADEC (ECU) that has two channels. No more information, I am afraid.
Originally Posted by FCOM 70-20-A
FADEC has two-channel redundancy, with one channel active and one in standby. If one channel fails, the other automatically takes control.