To clarify, I'm assuming the scenario is: remote client connects using VPN to XYZ network (i.e. where the VPN concentrator is located). Client then sends print jobs to appliance at XYZ successful, but no internet. Flip the checkbox and situation reverses. Correct ?
How is client connecting to internet - 1) via dialup connection to ISP, 2) dialup connection to XYZ modem bank, 3) broadband internet or 4) corporate network to internet connection?
Initial thought would be simply that there's an IExplorer proxy configuration in place at either the remote or probably the XYZ end. With the VPN tunnel up, internet traffic should be trying to navigate via that network adapter and the gateway it gets from the XYZ network if the remote gateway box is 'ticked'.