Rome did not actually abandon the 84-year cycle or March 25th equinox (which, of course, led to periodic differences in date between the Alexandrian and Roman churches), but often Rome seems to have accepted Alexandrian calculations. Not always, however. From time to time, the Roman church expressed its unhappiness with dates that it considered unsatisfactory. Ironically, every time the Romans consulted experts, they were essentially told that their way was inaccurate, and that they should adopt the Alexandrian computation.
In 325 CE, the Council of Nicaea met. One of its primary tasks was to ensure a uniformity of observation in liturgical matters, particularly with respect to the observation of Easter. The council decreed that Easter should be kept on the same day everywhere, and from the evidence of a surviving letter, it seems that the Alexandrian church was to make the standard calculations. Just because the Alexandrian church was tasked with calculating Easter does not mean they continued to rely upon astronomers to supply them with the actual date of the vernal equinox. Rather, they seem to have taken a number from the astronomers sometime in the 3rd century, and simply used it from then on. In 325 CE, for example, the equinox fell on March 20 (in Alexandria).