Checking doneness on a rotisserie is a little tricky. You'll get a lot of exterior color, but at this time of year, you'll be losing a lot of heat from the grill to the cool or downright COLD air. The stated times for the grilling will probably be too low.
Pick up an Instant Read Thermometer. They're fairly cheap, dial ones can be had for as little as $7 and digital ones start at about $13. Slip the rotisserie bar out of the motor so it's not spinning and stick the thermometer in the thigh meat between the leg and the bird. In a few seconds, the temp reading will stabilize and you'll know if it's done or not. Don't leave it in the meat as they're not rated to withstand cooking temperatures as are some other more troublesome thermometers. There are remote thermometers you stick in the bird and read the temp on a guage outside the oven. But with a spinning bird, you'll have problems with the cord.
Those pop up timers in most turkeys are set for 180 and you'll overcook the breast meat terribly at that temperature.
You should shoot for a temp of about 170 in the thigh and 165 in the breast, but usually, the breast is cooking faster than the thigh.