If I understand your question correctly you're asking how to advance Yui (green hair girl)?Thank you for reply. One more question: if progression with that girl is not tied to the cinema, then how do I progress with her? At first it seemed to be doing it just by going to the convenience store during the day when her "boyfriend" was there, but after unlocking the cinema with the two of them, it doesn't seem like that is advancing any further.
If so then you can't she is different from the other two that you meet at the dojo, however there is another scene with her that is also CG but you need to complete some steps before to get that.
You already talked overheard the conversions with the dude that visits her during the day now what you need to do is go to the construction site at 00:00-01:45 and once you're there you should see shadows in the top left skip time and get to 02:00 and you will bump into Yui, repeat this 2 more times and at the 4th time you come and around 00:00 - 01:45 just click on the shadows and Yui will let you join them.