For sure the Garden State trains were solely a PRR operation, operating entirely on PRR trackage (the Bridge Branch was PRR to Vernon). The article "Riding the Pony Express" in West Jersey Rails II mentions that power off the race trains to Garden State was run light to the Camden Engine terminal via Jersey for turning and servicing even though move would have been shorter via Vernon and mileage on the PRSL (resultiing in increased expense to the PRR). Likewise, the Stroup book also mentions that the Garden State trains were "strictly a PRR operation" (pg. 19).
Regarding the Atlantic City trains, the Stroup book merely says "they were regarded as PRSL trains" (pg. 18). Hard to say for sure if this means operationally, financially, or the perception of the general public.
The WJ Rails article states that the AC race trains were run as passenger extras. If so, they would be crewed off the pool and not advertised for bid. Since the last season for the AC race trains was 1967, they were gone by time I hired on the PRSL in 1969. However, granted my memory by now is a little foggy, but it seems to me that guys I worked with in those years would frequently refer to the days of getting the dream call in season to work a race train, both in train or engine service --- the bigger the horseplayer, the bigger the regret that the trains were gone.