common: ReloadTokenAuthenticator: Fix race condition
Description
The shared variable must be modified only while holding the mutex for the condition variable to work correctly. The variable no longer has to be atomic as it's no longer read while not holding the mutex.
Validation
Please note steps the reviewer should take to be able to test this MR; any necessary setup they might need, what results they should be looking for to verify.
Issues addressed
Closes / Resolves / Addresses (delete as appropriate) issue <e.g. repo-name#x>