I'll preface my comments by saying I have never grown an American wisteria - but do successfully grow both a Chinese and a Japanese wisteria as 'trees', and have read widely on wisterias in general. Peter Valder is considered one of the world's experts on them and his book on wisterias is the best thing I've seen (IMO there's a lot of nonsense written about them by people who've clearly never grown one successfully themselves!) Peter Valder (from Australia) appears not to have direct experience growing the American ones either but this is what he has to say about them:

'Flowering as they do on current year's growth, the American wisterias do not usually display their flowers well if grown on pergolas, though the long-racemed introductions of W. macrostachya may prove to be exceptions in this regard. In general, however, they are seen to best advantage against walls, around verandahs, over fences or as pillars on wooden or metal supports. Under these conditions they may be pruned to keep them within bounds at any time of year. However my experience with these plants is such that it would seem unwise of me to be dogmatic. I suspect, though, that two or three light prunings during the growing season may lead to greater floriferousness than a severe cutting back in autumn or winter.'

Aunt Dee is a W. macrostachya (macrostachya means 'long spikes') so is of the kind he's saying would be suitable for a pergola. It is generally said that the long-racemed types display best on pergolas or grown as 'trees' with tall trunks so the flowers have space to dangle freely - how tall is your pergola? Could someone pass under it when the wisteria is in bloom without brushing through the flower racemes? (bees love the flowers!)

Checking information on various US Extension university sites, pruning after the spring flowering is generally recommended. From my experience with wisterias, I'd say wait until spring flowering is over and them prune the whippy, curly new growth back into the desired framework as often as needed during the growing season to keep it neat and promote flowering. I suspect that even these 'new wood' flowering wisterias may develop the short woody spurs that bear a lot of the flowers. Pruning the new growth back regularly certainly promotes the development of those growths in the Asian wisterias so I'd guess that it would be good for the American ones too.

The other thing I'd be sure to do is to remove and seed pods that you see after the leaves fall and the pods become visible. You really don't want them to seed themselves around. That is probably as true for the American ones as it is for the Asian ones - and perhaps even more so as the American ones are said to be hardier and, one would assume, therefore more likely to germinate well from seed!

These are awesome plants! Don't prune until after they bloom though. They bloom really well here in May. I have never seen the re-bloom that is claimed for these. That is why I'd wait about pruning.