The "old spin balance" would spin the entire assembly, with new tire/wheel mounted on the trailer. In this case, all parts would be balanced, tire, wheel, and drum. Using this method, you need to mark wheel to lug bolt, after balance, before removing wheel again, to be sure the tire/wheel is remounted to drum, exactly as before removal.
Lots of opinions on trailer wheel balance need. IMO, the way many shops balance trailer tires/wheels, does little good. Using the lug type balance, should be helpful.
Jerry