I'm out of space and SpiderOak keeps showing me the "exceeded space" message when I go to other tabs

If you're trying to delete data and nothing is happening, then there might still be uploads stalled in the queue which are blocking your deletes. Every time you modify a backed up file, save a change to your backup, or perform any other action on SpiderOak, these actions are placed in your queue in order. If you still have uploads in your queue, then these will keep trying to complete before your "delete" actions can go through.

In this case, you need to clear your queue. Now you will be able to delete files until you no longer exceed your space limit.