To put it simply, ESDs and Phantom Faces do not work together at all. You can't push items into a Phantom Face using a ESD nor extract from it, even when the tooltip says "connection is fine and working"

Versions:
MC: 1.10.2
Forge: 12.18.3.2185
AA: 1.10.2-r88

They DO work, they just won't assign their slots appropriately by default, so you need to set them yourself, and then it's fine.
But this works in 1.11?

ohh, ok. And yes, in 1.11 the esd sets the slot number automaticaly

Just tested on 1.11 and it works fine