I can't comment one way or the other definitively on wire type from the photo given.
But the connector on the PS is for a jacketed/sheathed cable. As those cables flex over gime with starts the connector will cut into the insulation and cause an arc/short. May take weeks may take decades but it'll happen eventually. It will also allow moisture into the PS and cause it to fail prematurely. To run those wires into it as is, a grommetted connector would be better. Something with a strain relief and a neoprene seal that tightens under compression.
