Given that the VPN headers around each packet will take up space and then disappear, they could be looking at packet size vs MTU to come up with a way of guessing (it would be a wild guess) that the user is behind a VPN because their packets are consistently smaller than other streams.
An even wilder guess would be that they are looking at round trip time (more precisely, how long from when a tcp ack is sent to when the next packet returns). Most computers are fast enough to turn around in microseconds. So for a given host (single IP sending requests) if some/all users are behind a vpn that really leads off to distant parts of the world, the variation in RTT will be huge (120ms for some, 30 ms for others, etc) which can form a fingerprint of who is unique and what might be a VPN vs just a NAT (where there are many users but the RTTs are almost identical.)