Strange 100% knows they're dating. It's just that his dark half is a completely callous asshole who's perfectly fine throwing people under the bus if it helps get what he wants. And in this case, what he wants is people to pay attention to him and help fulfill the super needy part of his personality.

"I don't want you to visit," Strange whines a little, as he lets Yuya grab onto his arm. "I want you to stay there. You, Lambert, Rita, Tyki...I want all of you to stay in England and stay with me."