Rockblock satellite modem to Teensy MCU UART communication problem (multiple power sources)

I’m using an mk1 rockblock modem, which is using a sub 0,1″ connector, thus I got a special cable with the kind help of Rock7mobile. After getting a cable, the modem has been powered with a power supply unit (not through the USB cable) for the first time, with a link on Teensy Serial2. However it doesn’t work. Note that the Teensy is still powered through the USB cable.

I’m sending “AT” commands to the modem, which are reflected back… Mixed with some gibberish sometimes.

So I first suspected the lines were noisy one way or another (it’s a prototype, so wires are loosely connected on a breadboard).

Sometimes, the modem returns an error, meaning the transmission went bad from the uC to the modem, sometimes it’s the other way around. Are lines noisy ? Is it a problem with CTS/DTS ? The lines are floating right now, however the documentation for the 9602 (the Irridium module at the heart of the Rockblock modem) states that CTS/DTS are ignored when in command mode, which is the case when sending AT and getting a reply. Is the modem itself at fault ? What am I missing ?