Planted the bulbs late last spring .... has developed cluster of tubes that have grown to what appears to be maturity.
No blooms !?
we are in zone 7 (Richmond, Va) and am seeking what to do to care for the plants over the winter.
Dig up the bulbs?
Cut back the tubes - when?
Fertilize when and with what?
Leave as is and cover with mulch till spring?
Would like to get some blooms next year !!!

They should be fine in the ground over winter. Surprised they didn't bloom as bulbs; when bought they should already have the energy potential and size to bloom. Did you plant them at the recommended depth?
Not for sure what you are describing with the term 'tubes'. If you are referring to the flower scape, they usually fall off in fall; or you can remove them at your leisure.
I don't think I've ever fertilized mine, most reliably return yearly. Check the planting instructions for their recommendation.
I'm in a colder zone and not all the ornamental alliums return. A. schubertii, A. caeruleum, A. christophii, and A. karataviense are ify for 2nd season bloom at best (for me).
The tall big round ones are reliable returners here.

I have the big tall round ones too. Are your's planted in full sun? If less than 6 hours of sun a day, they may not bloom. And planted too deeply would also inhibit blooming.

There is no need to mulch or give them any special care.