well you can hit win+r and type cmd
then type netstat -n
you should see something like this
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so in my case you can see the DHCP address the wireless router provided connected back to my openvpn server
then a bunch of connections to 192.168.3.6 (openvpn address)
you need to be sure you configure your vpn correctly for the purpose in my case for example openvpn doesn't by default route everything thru the vpn you have to push the redirect gateway directive to route web traffic thru the tunnel.
I'm not super familiar with your vpn solution so you need to double check if it redirects everything by default or if you need to configure it to do so.
while you won't see a difference (hopefully) using the web over the vpn the security benefit is that everything you are browsing at the public hotspot will be encrypted back to the vpn server so if anyone was trying to eavesdrop on the public wifi they would just be seeing the encrypted traffic with no real way of telling what the heck it is, where as without the vpn they could capture everything you are browsing, and steal passwords ..etc...