My TYLT and Note 5 don't place nicely in portrait either. I've had the TYLT a while.
This is with and without a case.
Sometimes I put it on absent-mindedly in portrait and I see a green light. I've noteicedin these circumstances the base of the phone is a few mm away from the front of the charger. My guess is that the coil (on the Note 5) falls quite close to the top edge of the TYLT charger and the angling on the phone means it just charges.
I've experimented with putting something at the bottom of the charing cradle (e.g. a piece of paper) to guarantee the angle. However, so far, no success.