Eh ill say this to clear things up: in my high school there were girls who were 18 who looked 14. Also, some girls just are naturally short and cute so they seem young but aren't. Its not like every girl or guy matures at the same pace or fits your socially defined version of what an "18 year old" looks like. That said, thr guy doesn't seem like a lolicon so if she really did look underage to him I think he'd have asked for her ID cuz that's an excuse to go to police and child services.
On a different note, this manga is quite cute. Her resourcefulness is a bit over the top for some girl he just found but seems like both people have their share of family issues.