Sounds like you're hoping for an Agent (like MSSQL and Oracle and Sybase, etc).
Unfortunately I don't believe that there is an Agent for MySQL.
Here is an idea that might be a step further for your situation.
Setup a policy that allows 'User' backups 24x7.
Modify your script that does the MySQL export and add a command to initiate a 'User' backup (using the /usr/openv/netbackup/bin/bpbackup command).
That way, as soon as you export the DB to file, you immediately send it to tape. No waiting for nightly jobs to pick it up!
Hope that's vaguely helpful,
$0.02