The existing leviton 4 way switch is in the middle of the run, if that matters. There is a 14-3 entering and a 14-3 leaving the box. The two blacks are nutted and there's no power directly to the switch. The 4 remaining red(2) and white(2) wires(travelers) are connected to the switch.

The exiting screw orientation is: 2 bright penny color screws at the top left and right and 2 dull brass screws at the bottom left and right. One set of wires are connected at the top: red right and white left. The other set of wires is connected to the bottom: red right and white left.

The new lutron switch screw orientation is diagonal: 2 bright penny colored screws at the top left and bottom right and 2 dull brass screws at the top right and bottom left.

Should I match the existing screw/wire connections which means the pair of wires will be diagonal to each other than normal like the existing since the matching screws are on a diagonal?

Since these are travelers does the orientation matter?