We are using "Always On" and only take backups on one server; actually the primary server.
There isn't a need to take backups of both servers because if the Primary server "dies", as you indicated in your scenario the Group would failover to the other server and you would run your backups there.
Our configuration is like this:
-the same backup job is on each server
-the 1st step in the backup job is the check to see if the group is on the "primary replica". I wrote a function that checks for primary replica which accepts the "group name" as a parameter.
-if the group is on the primary replica the backup runs (step 2); if not the job just exits
This can work either way, say you wanted to run the backup only if the group were on the "secondary replica" then continue.
1. We didn't use the backup wizard to create our backup jobs, just good old sql scripts.