Then Tibbers instantly returns to Annie
Not sure if glitch or intentional

Depends on your situation. If your running away from tibbers as he is chasing you and annie is nowhere to be found that is normal because he can only chase you a certain amount of length from annie unless she is actively chasing you. Otherwise it is a glitch by the sound of your post you were running from tibbers when it happened so rest assured it is normal. I play as annie myself on both clients so it happens from time to time.