If I may add, the previous posting I made defines how should the setup be. But I forgot to answer your specific question: How to find out if the backup really happened?
When you have defined the TDP for SQL environment properly - and again, a clustered environment needs more attention - TSM logs would have been setup. These logs will tell you the status of your backup. It records mostly what has been done during the backup.
A TDP for SQL log would look something like this:
01/16/2007 20:20:29 Request : FULL BACKUP
01/16/2007 20:20:29 Database Input List : *
01/16/2007 20:20:29 Group Input List : -
01/16/2007 20:20:29 File Input List : -
01/16/2007 20:20:29 Number of Buffers : 3
01/16/2007 20:20:29 Buffer Size : 1024
01/16/2007 20:20:29 Number of SQL Buffers : 0
01/16/2007 20:20:29 SQL Buffer Size : 1024
01/16/2007 20:20:29 Number of Stripes specified : 1
01/16/2007 20:20:29 Estimate : -
01/16/2007 20:20:29 Truncate Log? : -
01/16/2007 20:20:29 Wait for Tape Mounts? : Yes
01/16/2007 20:20:29 TSM Options File : C:\Progra~1\Tivoli\TSM\TDPSql\dsm.opt
01/16/2007 20:20:29 TSM Nodename Override : -
01/16/2007 20:20:29 Sqlserver : SQL1
01/16/2007 20:20:29
01/16/2007 20:30:47 Total SQL backups selected: 30
01/16/2007 20:30:47 Total SQL backups attempted: 30
01/16/2007 20:30:47 Total SQL backups completed: 30
01/16/2007 20:30:47 Total SQL backups excluded: 0
01/16/2007 20:30:47 Total SQL backups inactivated: 0
01/16/2007 20:30:47 Throughput rate: 5,016.35 Kb/Sec
01/16/2007 20:30:47 Total bytes transferred: 3,153,774,624
01/16/2007 20:30:47 Elapsed processing time: 613.96 Secs
The above is an actual snapshot of my TDP for SQL server backup.
There is a TSM GUI interface called TDPSQL.exe. If you have confidured your cluster environment properly and have defined the right OPT files for the shared resources, the TDPSQL.exe GUI interface should open. From here, you can see all backups that had been completed whether incremental or full. This is another way of finding out if the backup ran successfully.