Yes, they can see the domain name. So they can see that you visit pornhub.com 3 times a day, but not what you are watching.
Also I wouldn't worry about it too much, a lot of routers doesn't have a history option and it has to be enabled on most of them.
But if you are worried, get a cheap VPN like Mullvad. You can see a list over trusted VPN providers here: https://www.privacytools.io/providers/vpn/.
I was thinking "This is just a good Photoshop. There's no way."
And the summary does, indeed, sound reasonably wholesome for a pulp romance.
HOLY HELL THAT'S AN UNFORTUNATE COVER, THOUGH.