There are two types of users: those who want reminders from every folder and data file in their profile and those who don't. Beginning with Outlook 2007, Outlook supports reminders in any folder and across additional .pst files while Outlook 2003 and older support reminders only in the default folders within the default mailbox or data file (unless you use an add-in).
If you aren't getting reminders from other pst files in Outlook 2007 and up, you'll need to enable reminders in the Properties dialog.
Right click on the top of the pst file and choose Properties, then enable the option to "Display reminders and tasks from this folder in the To-Do Bar". You'll need to restart Outlook for the changes to work.
When the 'Display reminders' setting is not enabled, you'll see the following warning message when you set a reminder or flag an item in a folder within the data file: “The reminder for “<subject>” will not appear because the item is in a folder that doesn’t support reminders. Is this OK?” (This message may also appear if you create an appointment in an iCloud calendar (if using the icloud addin), you can ignore the message.)
Enable Reminders in other personal folders files tutorial
Disable Reminders in Other folders
I've had several people ask if they could revert to the Outlook 2003 behavior, where reminders did not fire from non-default folders. Unfortunately, this isn't possible. If the data file is a delivery location (in Account Settings, Email accounts tab), reminders will fire from all folders. If you deliver an account to the pst file, reminders are enabled by default, plus tasks and flagged items in the pst are displayed in the To-do bar.
If you don't want flagged items or tasks from other pst files displayed on the To-do bar, create a custom view to show only items from certain folders or data files. If you want to disable reminders in non-default folders, either don't set reminders on the items or move them to a new pst file (and disable the option to display reminders).
We have a VBA code sample at How to Remove or Change the Reminder on All Day Events that can be tweaked to remove default reminders on appointments created in other folders.