To add, unlike other actions performed during a FATE, healing/shielding/buffing doesn't require you be synced to the FATE.
In order to participate in a FATE, you must sync to it. If the FATE level is close to your level, you automatically sync.
If the FATE level is not close, you must manually sync.
The FATE is a level 39 FATE, as a L54 healer it is easy to start concentrating on healing and forget to sync, as you can still heal the group or others outside the group while not-synced.
As others above said, you need to do at least one point of damage in order to be added to the enmity table of the FATE and you can only do damage while synced.
I have flubbed this a few times, forgetting to sync and try to participate
...oops.
So, always double check you are synced before attempting a FATE, in party or not.