Multiple traffic groups with HA groups

If the traffic group is active on BigIP1,you should not be seeing traffic sent to BigIP2. Have you taken a traffic capture at the time of the failover to see if the BigIP is sending out Gratuitous ARPs? The easiest way to troubleshoot this would be to open a support ticket. You can reach support by calling 1-888-882-7525 or internationally 800 11 ASK 4 F5. Make sure you have your BigIP's serial number available as you will need it to open the case.