Creating reminders with additional Criteria

I know Reminder sounds more like what you want but I think in this case you may actually want a Subscription.

How do you have the users set up in your app? Are they separated by role at all?

What you would do is set up a report that contains records that the users would need to work on. So it sounds like a report with filters for cases that are in an "Open" status and some specific referral source.

If the users that you want to be notified of those cases are the only users that have access to see the records then you could simply send it to "all users with access" then select the report above and this will only be sent to users that would see a record in the report. You will likely want to test this first to make sure it works as you expect it to. 

That is assuming you want it to be automated. If you just have a list of users that rarely if ever changes that work these groups of records then you could just put their emails in their and be very specific. If the emails are for outside your organization it will probably stop you from creating this. In that case you need to contact Quick Base support and let them know you want to be able to send Open emails, emails to any domain not just your companies.