As Paul said, the collection "Run now" button also initiates migration (
after the collection runs). To add to that, you'll notice that the event log message will tell you not only how many files are collected, but how many are migrated as well. The event will have a description which contains something like this:
263 Saveset(s) were Collected into 4 Collection(s).
1 Collection(s) were Migrated to secondary storage.