"When you are finished filling the barrel, how do you prevent back flow from coming back down the hose towards the pump?"
First, there's the 1-1/2" gate valve on the bottom of the barrel.
Second, each end of the 3/4" hose from the Flojet to the barrel has a full flow garden hose shut-off valve on it. I ordered the full-flow valves from Amazon since the local big box stores didn't have them.
Actually, when the gray TT tank is empty the Flojet will pump air and it will blow out the 3/4" hose. So if you close the valve at the Flojet, shut it off, and close the two valves at the barrel there's very little water left in the line. You do have an ounce or so in the Banjo fitting when you disconnect it. That's why I flush the line with gray water after I run the black tank out.
All the plumbing and pump are in the TT. As soon as I get it back from the repair shop (another story) I'll post some pics on my Webshots page.