Actually, if you look at the Team interactions previously, it is only normal.
Lee was always the most empathic out of them all, so he is the one who cried.
Although same spirited, Gai has been through this before, so it’s only normal he’d react this way.
As with TenTen, she was always strong-spirited like Neji. If we reverse roles, for example, the one still crying would be Lee, Gai acting the same way as he did now and Neji, although moaning the loss of his team-mate would react the same way TenTen did.
Look back at Kazekage rescue arc when they were doing that phase with hand tapping. TenTen and Neji were the ones more reserved at the idea, while Lee was the one who quickly followed, in excitement.
So yeah, I find it normal.