Upgrading from 5.2.1 to 5.2.2 is a minor change, and is what IBM considers a "level" increase. From my System/370 days, I remember that IBM classified its software products as "Release.Version.Level", so TSM falls in this category. We have upgraded our TSM Host Server from 3.7 to 5.1.9 and it supported all our TSM clients which were at 4.2.1. I believe you won't any trouble upgrading from 5.2.1.3 to 5.2.2.5.
Raymond