Routing should not depend on the service. Routing table is used to figure out what path to take to reach a certain host/network. You cannot route certain services (using one set of ports & protocols) to use one route while other services to use another route. Even if I don't know something, it will be not so common.
What is possible, however, is that split tunnel is used. It heavily depends on how router is configured and what VPN software you are using (whether it allows overrides). In most cases network administrators don't like split tunneling and (as you'd like) route all the traffic through VPN prohibiting any overrides (unless another VPN client is used :-) ). While it is more secure, it is a pain to work and let's say stream music at the same time.
You can use traceroute command to see what path traffic is taking for a particular destination.
You can try to change default gateway and direct all traffic into VPN once connection is established. However this would depend on whether there is a route to the internet on the other site for VPN connections as it may know local network only.