Did they send any kind of instructions for setting it up?
I had similar issues with my JET quad before I went to FAST system.
I don't know exactly what the issue was with it emptying the float bowl/acc pump well, but it did happen everytime it sat for a week or more. I don't have the issue with my old 76 CC 454 w/ factory quad...it will fire up within seconds even after sitting a couple weeks.
Proper procedure for a quad is to push the gas pedal to the floor, let up, push it again 1/2 then let off...this should close the choke plate (the smaller plate in front of the carb that covers the primary throttle bores) and give the engine a couple shots of fuel from the accelerator pump. That choke plate should just be closed by the bimetal spring under the black plastic or cast aluminum choke housing on the pass side of the carb. That spring contracts when the engine is cold (less than ~60* degrees and it should close the choke plate fully) and expands (opening the choke plate) as the engine warms up. It needs to be supplied by 12v ignition switch on/run to open the choke coil up, and that should take about 4-5 minutes to open fully. If the choke plate isn't closing at cold temps you can adjust that housing to move the choke plate...when making that housing adjustment, the throttle should be opened 1/2 way or more to allow the high idle linkage to operate the choke plate, and to set the cold idle speed cam for a higher idle, that is controlled by a screw (on the pass side of carb down towards the baseplate...usually a torx head screw facing the front of the carb) shoot for 1500 rpm when on cold idle. As you crank the engine there is a small vacuum canister (choke pulloff) that is on the front pass side of the carb that should open that choke plate about 3/16" to allow some air into the engine while cranking/cold running conditions..make sure that has a good vacuum line and the canister actually works...its not uncommon for them to leak as well, and not allow that choke plate to open.
The fuel draining from the bowl is the bigger issue here, I don't believe it would evap in a weeks time, but rather its leaking into the engine...so watch your oil and give it a sniff test if you've had a lot of fuel drain into the engine it could dilute your oil and be explosive. If this has only happened a couple times I wouldn't be too worried about it.
check the fuel pressure while cranking to make sure fuel is getting to the bowl, if sufficient, then check the acc pump squirter to see if its shooting gas into the carb when the linkage is cycled...if not then you need to figure out why its not getting into the bowl...like a sunken float that won't allow the needle off its seat and allow fuel flow.
then proceed to figure out why the fuel is draining out of the bowl as well.
Good luck John!