In Project Almanac, the group made a pact/promise that they would only go back together as a group, never individually.
At the music festival, when David doesn't kiss Christina, he goes back on his own because he knows that she wanted him to at that moment and they could be together.
I get that he may be embarrassed about the whole thing, but why doesn't he just put it aside and get everyone together and explain that they need to go back? He could even tell Christina that he missed the moment at the festival but he can fix it.
Also, why does he actually go back to that moment at the festival to kiss her, why doesn't he just kiss her in the basement and tell her how he feels, surely they'd get together then anyway?