Some cutouts are labeled for POS ground others NEG ground HOWEVER that shouldnt cause the relay to stick right off the bat, although it can affect its longevity. They can be adjusted to some extent (air gaps and/or spring tension) but a new one shouldnt require that.
Make sure the relay has a good bright clean shiny GROUND, it needs that to work properly.
Id double check alllllll the connections, especially on cutout and then the ammeter and to the battery. The initial reverse current out of the battery into the genny is supposed to assist in causing the relay to drop out.
One can replace a mechanical cut out with a solid state diode type of device and those usually work decent........
Make sure its wired correct, BAT to ammeter and GEN/ARM to Gennys ARM post and check the ammeter wiring and its connection to battery source. INSURE A GOOD GROUND