Regulus took the tea rather cautiously. Because it was hot, because he didn't know how the bags work (where was the teapot? he was pretty sure a teapot was supposed to be involved in this process), because he really didn't know Duncan- even if he'd watched him make the tea. Regulus was just uncertain about everything right now, and it was easier to let the cup cool a bit before he tried it. It did help settle his unease when Duncan tried the tea.
Also, Regulus was mostly focused on what Duncan was saying.
"Oh," he said when Duncan revealed he didn't have magic, and then Regulus dived right into the deep end of his thoughts.
He was stuck in this place, without a wand. He'd been given clothing and shelter, and the staples of food and the tools to work those staples. But he lacked the skills necessary to work those staples into even the simplest of meals. Not even a meal, even. He couldn't manage toast on his own. The tools at his disposal either confounded him or frightened him and trial by fire in this sense was potentially hazardous to, well, everyone.
Regulus didn't get to pick and choose who he associated with, he didn't even know how to find the few people from his world because he didn't know how to use the phone, much like he hadn't known how to use a toaster.
He had to just accept the help of anyone willing to help him no matter how much it made him uncomfortable.
Even if they were muggles.
Especially if they were muggles - they were the best resource for knowing how to use muggle inventions. He had to admit, even having a wand wouldn't help him with that.
"I do," he finally said, admitting he could do magic, but he skipped over that and rushed on to say, "Are there people here who could teach me how to cook? Could you?"