These are considered codeshare flights. Other than reservation handling you will not really be interacting with Virgin Atlantic. You will be on a delta plane with delta crews and delta services. You will also check in with delta.

If its an hour connect on the way back, it will not be enough time due to having to deal with Customs and Immigration and that can take a long time depending on how many flights arrive at the same time as yours.

An hour on the way out is kind of tight as well and if your first flight is delayed you can miss your flight.