VPN and Wifi
Short answer: Completely normal - in fact one is more likely to want to have VPN turned on when connected to "public" wifi. In general when you are connected to a VPN the outside world will be told that your IP address is the IP address of the VPN server - so your real IP address is hidden from everyone except the VPN provider.
VPN works in addition to whatever network connection you have (wifi,ethernet,usb,hotspot,...) by creating an encrypted "tunnel" between your device and the VPN server. All your data that is sent through that tunnel cannot be read by any device on the networks that the tunnel traverses. So it's a good safety precaution in many circumstances. But what you need to be aware of is the provenance of the VPN provider because their server sees the decrypted data as part of transferring it to and from the real destinations. However.... any connection you are making via https or ssl creates its own encryption between you and the real end point server (eg. with internet banking) - so the VPN server can see that you're connecting to your bank but they can't read any of the messages between your device and the bank. ie. multiple layers of encryption.
How are you making a network connection, if not over WiFi? Do you have an Ethernet connection?
Your IP is safe as long as you are using the right VPN. VPN is basically a necessity nowadays. Most websites and streaming channels are Geo-Blocked in your country and only available in certain countries. Not just that but you also need a VPN to stay away from prying eyes, ISPs and hackers when you are at coffee shops and airports where you are most likely to connect to a Public Wifi. If you are looking a Good VPN which is highly affordable and packs in the latest features then you should consider getting Ivacy VPN. I did my research and found out that Ivacy VPN is built for High-Speed VPN connection so that you can enjoy seamless Online Streaming, Unlimited Bandwidth, and a Secure Web-surfing experience. You can get Ivacy at 77% off on their 2 Year Plan.