I don't see how the programming of the valve is involved either.
Lets say the valve was in the solar on position (when the pump turns off), then the solar feed pipe would be connected to the output of your SWG. When the vacuum relief valve opens up the water in the solar feed pipe drains back though the SWG, filter, and pump to the pool. The water in the return solar pipe would drain back to the pool though the pool return line.
If the Solar valve is off with the pump off, then the solar feed pipe would be closed and a column of water would be sitting above the closed valve in the feed pipe. When the vacuum breaker valve opens up at the panels then the water in the panels drains back down the solar return pipe causing water to flow through the Tee junction with the returns on one side, and the output of the SWG on the other side. There's probably less restriction on the return side so more water will flow there, but there's nothing to prevent back flowing through SWG, filter, and pump while the panels are draining. Once the water column in the solar return pipe drains down to a level that is below the top of pipe in your SWG loop then all the remaining water will return via the pool returns.
But even when the system is off for a long time you have a filter that is full of water and the top of the filter is 3' or so above ground level. The SWG pipe loop on the filter output is above the top of the filter and since water doesn't flow uphill the filter will not drain out back through the output. So you have the weight of the water in the filter trying to seek its level, which is the pool level and it will drain back through the pump to the pool. As soon as it starts to drain back down the output side of the filter will be in vacuum. If the output side of the filter is full of water then you're fine and you have a closed loop of water. But there's likely a vacuum breaker on the panels that will let air into the system, and there's also the leaky O-rings on your Solar valve that will slowly let air in when the pump is off.
As the air is let into the piping on the outlet side of the filter the water in the filter slowly drains back into the pool via the pump, and as the water leaves the filter it will gulp air back in from the outlet side piping.
You can try and replace the O-rings in the valve as a first step and see if that helps, but I don't see how that will completely eliminate the back flow issue.
I still think the proper way to fix the back flow issue is to add a check valve in the pump outlet line. That will stop any back flow and filter draining regardless if the output side is open to the atmosphere when the vacuum relief valve is open.