The word «дівчина» can be stressed either way (ді́вчина or дівчи́на) without change of the meaning. The printed version of «Академічний тлумачний словник (1970—1980)» only has «ді́вчина»: http://sum.in.ua/p/2/298/2 — however, in modern language both ways to stress it are acceptable, and the online version of the same dictionary, interestingly, marks both places of stress as acceptable: http://sum.in.ua/s/divchyna
Yes, the accent really depends on the dialect. People closer to the West are more likely to shift stress to the penultimate syllable, because of the Polish influence; and people closer to the East are more likely to be influenced by Russian. So, the accent «дівчи́на» might be an influence of Western dialects (although I can't vouch for this!).