Hello Jeff,
there are 2 scenarios where that can happens:
1) you create the "System Log", "System Load", "System Migration" with the arssycr command
2) with the Windows Admin Client, you export an application group from one server to another, and you check the check box "without storage set"
then in both case you are without storage set in your application groups.
In that case, everything will go to the cache. No protection from TSM.
Now, it is possible to move the data from the cache to your desired storage set, that means basically using arsmaint. Now I need to get to my note, because there others steps to make too.
Sincerely yours,
Alessandro