HUM in Signal path of Pedalboard due to Voltage supply

Good evening, everyone,

I have a rookie question, but please don't laugh at me now:

I built myself a pedalboard for my electric guitar. On it are three devices, which all need different voltages:
One needs 12 Volt, one 9 Volt and one 9 Volt but with plus and minus pole inverted.
So I bought a 12 Volt power supply. The line splitter itself on two ways on. One goes directly to the 12 Volt consumer and the other to a 12 to 9 Volt voltage regulator.
Works fine but as I told one device needs the 9 Volt inverted. So I took a y-splitter cable and on one output path turned the wires around. This also works fine but unfortunately I now have a hum in the signal when I connect both 9 Volt devices. If I disconnect the inverted one the hum is gone.
I suspect that this is a ground loop. If I hang a DI box at the output and press the ground lift switch, the hum is gone.

Therefore now finally my question:
Would you just use the DI Box and leave everything as it is or can you solve this better by inverting the 9 Volt so that there is no humming at all?