On the application it says "I authorize pre-employment testing for the presence of drugs/alcohol and understand and agree that the results will be released to" Company B. My start date is supposed to be December 2, maybe I will hear about it by then. Like I said before I already have a start date, and normally I find out right after I accept an offer. Is the first day still considered pre-employment?

The offers are comparable. There are pros and cons to both regarding the job itself. I think my best course right now is to take the DT for company "A" (subbing) and see how that goes - first time - I have never taken a DT before.