Here is a little more following what you’ve just read:
Explicit statements or conjectures on the final lot of Mary begin with the last quarter of the fourth century – contemporary, therefore, with Epiphanius. But the witnesses touch the problem ever so lightly, with evident uncertainty. Tychonius, a lay theologian among the Donatists, independent enough to be excommunicated by his own sect, seems to have identified Mary with the woman of Revelation 12, and to have spoken of a “great mystery” in her regard.  Ambrose is more specific but equally unsatisfactory. Discussing Simeon’s sword of sorrow, he dismisses the idea that Our Lady died a violent death; such a thesis has no warrant in Scripture or history.  But Ambrose does not tell us just how Mary did leave this life. In a remarkable passage he presents, as one hypothesis, the yearning of Mary to rise with Jesus in case she was fated to die with Him.  There may be an insinuation here that the desire was not frustrated; against this conclusion is the flat statement elsewhere that Christ alone has risen once and for all. 
Paulinus, Bishop of Nola in Italy (d. 431), is anxious to learn Augustine’s mind on the exegesis of Simeon’s prophecy; he himself, like Ambrose, is aware of no document reporting Mary’s death by violence.  In his reply, Augustine mentions a previous letter of his own on the Lucan text; it is, regrettably, lost to us, but he does tell Paulinus that their views on the scriptural passage coincide.  Elsewhere, in several striking phrases, he makes it clear that Mary did die: she died after her Son; she died a virgin; she died, like Adam, in consequence of sin. 
Finally, however his silence may be explained, the fact remains that Jerome, who knew the local traditions of the Holy Land as well as Epiphanius, gives no indication that he is aware of any historical tradition with reference to the death of Our Lady, her grave, or an assumption.  Briefly, between Nicaea (325 AD) and Ephesus (431 AD) the allusions to Mary’s destiny are rare and insignificant.