UP Squared with the UPS and POE expansions module

So my question is if I have the UP Squared with the POE Module and the UPS /wide range DC HAT.

What happens if both units are say plugged in at the same time. I am working on a use case were i would need to have the ability to use either module depending on the situation.
I don't trust the operators to know, to only plug in poe or the 12vdc. (actually i assume if theres an open port, an operator will plug something in to it, regardless of directions)

Ideally i would hope the UPS/wide range DC hat would be primary power source and the POE would only be used when there was no other power.

Ive linked the two below accessories.

https://up-shop.org/up-peripherals/112-ups-and-wide-range-dc-in-hat.html
https://up-shop.org/home/245-poe-expansion-module.html