For some reason, the Captivate groups only work with contacts stored ON the phone. This also applies to setting custom ring tones.
One solution (from memory, phone is not in front of me) is to go to your contacts ->menu-> more or options and find the option to export contacts to CSV on SD card. Then re-import them (same menu) into the phone. The OS will link them so you don't see duplicates. Now you can assign custom ringtones and groups to the Phone contacts. Because like contacts are linked, it works transparently.
The only down sides is the groups don't get synced to Gmail if you use Gmail for contacts.