He always has this bored expression when the other contestants are singing. He will look around and into the audience. But when Vinit starts, his attention reverts to and stays on Vinit. He gets a really serious look on his face. Sometime, as mentioned, he'll mouth praises (usually in the middle of music - when there is no melody/lyrics), and gesticulate extravagantly with his hands.
To be fair, I think Vinit is a good singer who has genuine respect for whatever guidance HR has mustered. Not to mention, he probably carries a certain sense of gratitude/"indebtedness" towards HR for having reached this stage at such a young age.
BTW, did anyone notice that when AS gave Vinit the song "Tum Milein, Dil Khilein" HR bowed his head down as if he were hiding. Was he blushing?? 😈