Well first off this would depend on if she is a virgin or not? How old is she? And has she already had her period regularly before or is this the first time shes ever had a period?

no, she isnt a virgin, she has had sex only twice though so she is still very tight, she is also 17 yrs old.

That is pretty strange, I don't really see it being a major health issue, but maybe your hitting her cervix in a wrong way? Are you pushing too hard maybe? And is she actually really starting a normal period? Or is it just bleeding, (i consider a normal period, lasting for at least 5-7 days) I honestly don"t see how fingering can cause you to start your period unless you were doing something wrong.(if she never bled having sex, just fingering her shouldnt be causing her to bleed) maybe try doing it lightly and not going too deep in her and see what happens. If it continues, she should either stop, or see a doctor, (but by being 17 I can understand not wanting the parentals to know) go to a public clinic if you have to.