Judging by the pictures alone I very much doubt there's anything special about their power supply it looks like any one of the thousands available on AliExpress e.g.
They're okay, available in many sizes, a bit noisy with fan but highly prone to overheating without the fan. Note they have exposed mains connectors, not UK compliant unless put in another case which helps with the noise but increases overheating risk!
The datasheet says their 320W PSU can drive 26 fixtures so needs no additional headroom at all. going by that any PSU over 50W should be fine for four. I'd personally go to 24V 100W as that gives 4amps, and if they're 4 channels at 350mA they would need about 1A each with the drivers I linked.
(If you have a 12V PSU 50W to hand you may find they work just fine with that too, and run a bit more efficiently too. My suspicion is they only require 10V forward voltage)
Yes, those DMX drivers work fine with a range of input voltages. I run some at 24V and others at 48V
Joth