I use Firefox and the My Vodafone app together and haven't had this. I certainly haven't ever seen that message, just the one that tells you turn turn wifi off to set the app up (I don't think you need to download it over mobile data, just do the setup). The app needs to authenticate you, so needs nothing to get in the way. It's possible this is a spurious message and that something else is causing the problem.
In the first instance, try simply clearing recent apps - it's amazing how many problems this can fix. If that doesn't do it, clear the system cache by going into Settings|Storage and then phone storage, where there should be an option. If it still doesn't work, try restarting the phone. As a last resort, uninstall and reinstall the My Vodafone app.
I'm not aware of any 3rd party data managers that use VPNs, but VPN apps are available, and I'm sure you'd know if you'd installed one of those. It's possible something else is mimicking such behaviour and I'm hoping that the Recent Apps trick will sort that.
