Hmmm. A bit worrying. You are leaving it to chance there.
PSTs are attached to a Profile only if you connect the database with the Profile in the Mail bit of Windows.
If a PST database is not associated with a Profile, you should be able to add PST files in the Outlook Email area of Manage Data Sources.
I use a trick I picked up here some years ago, I create an extra Mail Profile, called Archive, with no associated email accounts. I then add to that Profile all of my extra PST files. X1 will then index them even when the PST file is not open in Outlook.
There may be other ways of achieving the same thing, including adding PST files directly, but I would not rely on having them open in Outlook simply because I don't want them open all the time.
You also refer to OSTs so I assume that you are using Exchange. Throw in the PSTs, and you have a complicated arrangement.