I'm making two gross assumptions here, which may or may not be accurate, but I believe they are since it'd be the easiest and cheapest way to make this adapter:
1) The adapter is using some sort of IC/PIC that is decoding each of the PSX's controller buttons into a seperate line.
2) The adapter is using some sort of microrelay to connect each of the button lines to ground on the Neo side.
For those who don't know, unless I've been vastly misinformed, the Neo uses a 'pull signal line to ground' method for controller signaling - negative logic.
The PSX uses a multiplexed serial line to transmit controller data - this is by necessity a positive logic system.
You'd need a relay or equivelant device to connect the signal line to the ground to emulate the proper controller signal for the Neo. Hence the relays.
I doubt that there would be extra relays inside the adapter, it'd be wasteful. A Neo would only ever use 10 (4x directions, 6x buttons). In-between the decoder logic and the relays, you might be able to swap say the select button and L1 or whatever would work better, but I bet you'll be stuck with those 10 buttons forever on this device.