if you're establishing a VPN connection, doesn't that mean your internet access is running through that connection? And if that's the case, would this mean that my employer can monitor my internet usage?
Yes. While you are connected to the VPN, everything you do goes through your work. Of course, this only happens while the VPN is connected.
From the menu bar, select . Click the lock icon in the lower left corner and authenticate, if necessary. Select the VPN connection from the service list. Click Advanced, then Options. Uncheck the box labeled Send all traffic over VPN connection. Click OK, then Apply. Only traffic directed to a server on the remote network will go through the tunnel.