I updated the unit through the USB cable and not through BlueTooth, and then rebooted it to factory settings (pressing down right footswitch + big central knob while powering up til it says [initia] or something like that) and now it works both with the original power supply w adapter and my pedalboards power supply.

I hope is all good from now on, cause the effects on this thing are crazy cool.

Thanks guys, and the Eventide support through email (Jerome)