Its a miscommunication because she heard one half of what he said and doomered about it.
And then he had the worst timing.
I'd honestly not even call it "he had the worst timing"
He just needed to put his foot down and say "no I won't stay over" to his boss.
We see his other coworkers fucking around in the backroom while he's not taken a break
working overtime, as a minor, and his boss is just being like "oh gee golly haha sorry I'm making you do this it's so weird how a bunch of people all got the flu on Christmas Day of all days"
The thing he did incorrectly was not prioritize his girlfriend, on
the Date Day of the year, when they had plans, he wasn't scheduled past a certain point,
and he already felt like something was wrong between the two of them.
I'm mostly upset that he apparently said "I'm taking all my breaks right now", because that implies he'll go
back to work and leave her again, assuming they even get a chance to talk and smooth any aspect of the problem between them in this moment of meeting up.
He should have clocked out when his shift ended. And he should have
walked out when he saw that text message. I know people in Japan put a lot of emphasis on personal responsibility and dedication to things like work and stuff, but it ticked me off more than anything else going on in this series at present. (Except for maybe her one friend just shitting all over the ML without ever having even met him, just to glaze the FL as the infallible perfect princess--mostly because it does nothing to actually help her, and might actually poison her toward her boyfriend and make it even hard for them to talk things out.)