The store isn't her part time job. Her family owns it. It's called Kotobuki Musical Instruments. She wouldn't "be there for a little inspection" if she was working there.I wondered if Mugi would somehow become a regular here, but it seems it was only a cameo and she isn't actually working there. Man, Mugi can't hold jobs, first this, then McDonalds.
On Chapter 7 Yukari saw the OG 4 when she was looking for the Light Music Club and interacted with Sawako and Nodoka.So cool! Gamma2015 said it well, she just takes over.
So now they've run into Mio, Azusa, and Mugi. Did I miss anyone?