Can the Wi-Fi owners see my history of iphone Wi-Fi usage?

I stay with boyfriend who has wig, just noticed VPN on top of my iPhone and was concerned of being observed through Wi-Fi, nothing to hide but more to b secure of bank accounts and such

Yes. If they are using a program from your computer or from their own computer with a permission to view your cookies, then they'll be able to know.

Just noticed VPN on top of your iPhone? You would have had to authenticate in order to be connected through a VPN. Not sure what you mean there…
either way it's possible for admin users of a Wi-Fi network to see your phones browsing history, app usage, and data usage, but only when you are on the network. Browser history from when you're not connected to that Wi-Fi is not visible unless you have enterprise grade software behind it.
The wireless router reads the traffic between your phone and the Internet, not the phone itself. Basic home wireless routers don't normally have analytics functionality anyways, it would have to be ano aftermarket router that didn't come from the provider most likely.