There is not a Nicene canon about the Calendar, and the reference in the Synodal letter only describes the fact that all would now celebrate on the same date as everyone else.
The main resolution during this period was that Pascha would be celebrated after the Spring equinox, and that Alexandria would provide the date. But on several occasions the Romans, who continued to do their own calculation, produced a different result and had to decide whether to stick with their own or submit to the Alexandrian. As far as I can see from a brief read, Alexandria and Rome carried out a correspondence on the issue of the date and neither mentioned any sort of Nicene authority for their own calculations. Letters from Leo of Rome show that he thinks the Alexandrian calculation is wrong.
It would appear that it was Antioch which used a different method and was the object of discussions at Nicaea and not any remnants of Quartodeciman groups. The issue here, as far as I can see, was what to do when the first full moon after the Spring equinox fell on a Sunday. And this caused problems all over the place, in the UK for instance, the indigenous Christians used a calculation which also used the full moon after the Spring equinox but differed on what to do in various circumstances. For a long period the calculation of Pascha remained a cause of some tension. Even in the 7th century kingdoms in the British Isles were divided on the matter.
As to the present practice of some Churches. I do not see how this can be considered non-Nicene. It is a matter of fact that the Julian calendar does not now reflect the actual date of the spring equinox as Nicaea envisaged. The Gregorian calendar does attempt to do so. It is more concerning that there are different Paschal celebrations, and it is this which might be considered non-Nicene. But the resolution of this situation surely requires that those Churches which use the Julian calendar also reflect on whether a disconnect between the calendar and the astronomical world was what the Fathers intended.