Re: Ai-hanmi tenchi-nage
Slide in on the 'earth hand/grabbed' side. Then Step in with the 'heaven' hand.
Syles may vary - FWIW, swing the elbow on the heaven hand into uke's center and raise the hand. Then rotate thumb down on the heaven hand as you step through. Your finishing posture should be on balance as if you were considering taking a fowrad roll with the heaven hand - now pointed thumb down.
With this approach you will get an 'up' and 'down' motion from the heaven hand and avoid the typical error of simply pushing the uke back with the heaven hand.
If all else fails ask someone from oyur school!