SQL Server AlwaysOn – Running SQL Agent Jobs on Secondary Read-Only Node

1. AlwaysOn secondaries map all reads to versioned reads, which are (almost) lock-free
2. Even with versioned reads there are some (few) locks in place, eg. schema-stability locks on obejcts. There is never any sort of propagation of locks from secondaries to primaries. Furthermore, there cannot be any propagation of locks from secondaries to primaries simply because the secondary is a back-in-time copy of the primary. There is no point in propagating a lock on object 'foo' from secondary to primary because the primary may had dropped 'foo' 2 hours ago and the secondary did not catch up yet. The propagation of locks downstream from primary to secondary goes through the log records and as such the locks are re-acquired on the secondaries when the log is redone, therefore the lock is always applied to the appropriate structure (if 'foo' existed on the primary when the lock was acquired, then by definition exists on the secondary at the moment the lock is re-played).
3. Secondary reads may block redo (eg. by holding on a schema-stability lock when the redo is trying to acquire a schema-modification). The redo resumes when the secondary reads releases the lock. And 'redo' in this context means 'applying log from the primary on the secondary', ie. catching up.

Within your SQL Server Agent job, have some conditional logic to test for if the current instance is serving the particular role you are looking for on you availability group:

if (select
        ars.role_desc
    from sys.dm_hadr_availability_replica_states ars
    inner join sys.availability_groups ag
    on ars.group_id = ag.group_id
    where ag.name = 'YourAvailabilityGroupName'
    and ars.is_local = 1) = 'PRIMARY'
begin
    -- this server is the primary replica, do something here
end
else
begin
    -- this server is not the primary replica, (optional) do something here
end

All this does is pull the current role of the local replica, and if it's in the PRIMARY role, you can do whatever it is that your job needs to do if it is the primary replica. The ELSE block is optional, but it's to handle possible logic if your local replica isn't primary.

Of course, change 'YourAvailabilityGroupName' in the above query to your actual availability group name.

Don't confuse availability groups with failover cluster instances. Whether the instance is the primary or secondary replica for a given availability group doesn't affect server-level objects, like SQL Server Agent jobs and so on.