It's complicated. Orders got backed up this spring and thousands of Model Ys and Model 3s were filling Tesla lots and not being delivered. This was (most likely) because of a shortage of radar parts. Then there was a wait as Tesla had to provide a software fix for "vision only" cars that don't have radar. After that, the floodgates burst and Tesla was delivering cars like crazy, ending up with record sales for Q2 (which ended June 30th). It seems obvious that some unfortunate people got bumped from the queue as Tesla pushed to maximize Q2 sales. Essentially, cars that were scheduled for early July deliver were diverted to people who may have ordered much later but lived where the car could be delivered in June. Or something like that. Or Tesla was being terribly capricious.
Things are still a bit crazy and some people have had to wait a very long time for their car (some even after being given a vin GRRR). I think it should get back to normal in a few months but that's assuming demand doesn't skyrocket. My guess is your SA is right and if you ordered now you would probably get your car in September or October or sooner. If nothing else wacky happens I expect the wait to get shorter and to get more consistent. Your SA is saying to expect a 2 to 3 month delay if you order in September. This sounds very reasonable.