Seems the apple watch 3 LTE won't work if my iPhone is power off or in airfly mode

Make sure that you have activated LTE on the watch. Set up and use cellular on Apple Watch Series 3 (GPS + Cellular) - Apple Support and set up service with your cellular carrier. Sounds like your activation was not complete and the watch is still tethered to the phone for calls.

Was this an AT&T corporate store, or just a reseller? Did they contact Apple during this time period? Were you trying to figure out why it wouldn't work without the phone, as stated by the other poster?

I spent 2 hrs at the att store trying to figure this out. Still no cellular.