My Arum italicum bloom in early spring. They should be blooming any time now. I usually wait until they go dormant during the summer to dig.
jim_6b

From the moment the fruits are red/orange and full grown you can dig up the tubers and divide them. Here in the Netherlands somewhere in september.
Gijs

I have these and I separate them in the summer. You live in TN. In different locations I would say different advice, but we live in the same zone and I waited til late summer. After the berries.

I found a HUGE patch a few years ago- The fruit was set & I dug down.. Bulbs had no roots so I gathered a bunch. Still have about 10,000 seeds now that I think about it.

... Perhaps I should plant those.