J.☯.
I'm right there with you. We worked for one week at home and then ventured out into the regular world (which Mommy desperately needed). We are still having some accidents, but he actually did better when we were out and about. He does have an older brother, and every time we went somewhere we all went to the restroom. That might have helped, because he was very good about waiting until we got to a restroom. At home he has some accidents, but he's getting better.
I would not use pullups just because you are not at home. I would absolutely keep him in underwear all day, no matter what. It really helps reinforce everything he is learning about his body and that feeling that he needs to go. If you are out and he pees into a pullups, it could take him longer to really get the concepts.
He might be ready to start stretching that 30 minutes into 45 or even 1 hour. If he has an accident, just shorten the time. It really won't be long before he is able to take the lead.
Sounds like he's doing great! Keep up the good work.
ETA - Pooping on the potty? What's that? I lucked out (big time) with my oldest. He protested the first couple of days and asked for a diaper to poop in. But he got over it, and the only time he had poop accidents was when he had diarrhea.
My youngest is finally pooping on the potty. The first couple of weeks he would just run off and poop in his underwear :-( That our he would strip down and squat on the bathroom floor. Hey, at least it wasn't the carpet! He's been much better the past few days.
I think you just have to keep him in underwear and keep cleaning it up. If he doesn't catch on in a couple of weeks, you could consider getting really cheep underwear from the dollar store and just throw it away. A friend of mine did that with her son. She said she was sick of washing out his underwear and just started throwing it away if he pooped in it.
Patience. Hang in there!