I've had this T6 about 5 months, and a few times I had a hard time at the gas pump where the pump would just shutoff as soon as fuel was flowing --
it acted like it thought the tank was full (it was 1/4 tank). Filling up took about 15 minutes....ouch.

Problem resolution:

(This may not apply to all 2013+ XC70s -- ours is the strict California Ultra Low Emissions Vehicle (ULEV 2.0) standard.)

Through experimentation, I found out that when you stop the car to refuel, you have to hit the "fuel flap" button before shutting off the engine.
If I do it in the reverse order, the tank is not ready to accept fuel. I believe it has to do with the EVAP Vent Valve being left CLOSED vs. OPEN when the engine shuts off.

Traditionally, this Vent Valve was a normally-open valve, meaning that it only closed during very brief testing by the EVAP system for a leak. The idea was that, when the car was parked, gasoline fumes would be absorbed by the charcoal canister and little would evaporate out the EVAP vent air filter.
However, the canister is an imperfect absorber, and the longer the car is parked, the more fumes are allowed to escape. But, this traditional way of valving, the car could be refueled any time (even with the engine running, something not recommended).

My hunch is that the environmentalist in some automotive engineer balked at this small emission, and decided the Vent Valve should be closed when the car is parked. The wrinkle is that, now the software needs to make a decision about your intention when stopping the engine...are you parking the car, or are you refueling? It has to keep the Vent Valve OPEN for refueling to work.

Thus, the importance of hitting the "fuel flap" button before turning the engine off, since this is the way the software decides to shut down with the Vent Valve OPEN.

I checked the Owner's Manual, and the info there is out-of-date, and gives a bum-steer saying to turn the engine off BEFORE hitting the fuel button. It's unusual to find a documentation error out of sync with the software. But, it could be something that was done special for the California ULEV standard??