They are exceeding the salary cap because of arbitration. That is one time OOTP's hard cap will allow a team to exceed the cap.
The extra cash in each team's budget sounds to me as if it is "cash from owner." Since each team would have similar market size and such (I'm going to guess you started this as an inaugural draft) -- the cash from owner would probably be close to the same amount each season, and sounds like a plausible explanation.
That's actually a much better hard-cap setup than most of the ones I've seen attempted on here, so congratulations on that!
