If you feel that he has taken to litter training in his space well, then you can expand his freedom (though I wouldn’t let him go all over the place just yet — unless you have a small place) and just supervise closely. The moment you see him lifting his tail to urinate you will need to stop him and escort him back to his litterbox. I’d also have a treat ready in my pocket once while he finishes his business in the litterbox.
Oh and when I say expand his freedom — I mean slowly, just give access to another room or hallway — whatever he can have access to that is nearest his pen so he can return to do his business, and then slowly expand.
You may find territorial markings at first, but piles of poo and urination should only be allowed in the box. This will really take some close supervision for the next few weeks while you expand his running space. IF you have a large space — like a full upstairs and it could take him some time to get to his litterbox, you may benefit from having a second litterbox he can have access to.
Even with litter trained bunnies I have had to give “refresher courses” by confining their area a bit. I also entice them to use their box more often (when their habits slide), by putting treats in their box throughout the day. So as not to load them up on sugar, I normally divide their normal amount of treats up into smaller bits. Like for example — One big juicy dried cranberry, and be cut up in quarters. I’d put a couple of the 1/4 size pieces in the on their hay in the litterbox, and I’d repeat that a few times.
I feel very fortunate as Vivian is amazing with her habits. We have a small home so it’s not a long way for her to go from the living room, through the dining, down a hallway to do her urinate. And that is what she normally does. I do have another litterbox in the foyer area off in a hidden corner, and she will occasionally use that. But that’s because when I first got her, that is where she was housed and so sometimes she will remember that area.
You also have to watch very closely if your bunny decides to jump up on soft cushy chair or couch. That can be a typical place for a bunny to urinate regardless of good litterbox habits.