Well, I suppose it is part of his job to be concerned and take care of her, and helping her 'cool off' after each performance would probably be a part of that. Sounds like a great job!
That ending though. Ah yes, the car just so happened to interrupt what she was saying, causing her to get all embarrassed. She's certainly quite cute, with some tsundere tendencies.
Yui-chan might be (1) Embarassed at her "cooldown" routine having been discovered by her Manager, (2) some Tsundere feelings might have awakened from her *cough-cough* "riding the Manager's magic stick", (3) Why Not Both?
Whatever the case, ... Do Your Best, Nakahira-kun. After all, It's GOOD To Be The Ki ... er, Manager (you Lucky Bastard)!