I can only speak for the Russian tradition. For a daily vespers,the Royal Gates would normally not be opened at all. Therefore, the priest need not vest in the phelonion at all, but just cuffs and epitrachilion.
Matins is a bit more complicated. Regarding censing, the priest does at least twice; once at the very beginning, and again at the end of the 8th Ode, when the Magnification of the Theotokos is chanted.Should there be Sunday Matins or a Polyeleos rank service, the censing is done at the Troparia of the Resurrection ("Blessed art Thou, O Lord, teach me Thy Statues...)" or Polyeleos. The Royal Gates would be open here and the priest would be vested in the phelonion . After the veneration of the Gospel(on Sundays) or the veneration of the Festal Icon, the priest returns to the altar and removes the phelonion.
In a daily matins service, the Royal Gates would be closed for the whole service. There is also the possibility of Matins with a Great Doxology chanted. If the Great Doxology is chanted, the priest opens the Royal Gates for it, vested in the phelonion. If there is a daily matins with the doxology being read instead of chanted, the Royal Gates remain shut and there is no dismissal at matins; the First Hour is read and the dismissal is given at the end of the first hour.
In my experience, few parishes do daily vespers and matins, so even though we priests learn about such services at seminary, rarely do we get the chance to serve them, outside of monastic communities and a few large cathedrals.
If all the above is not confusing enough, should a liturgy follow matins, the priest would probably be fully vested in all his liturgical vestments for or during matins. I do know about the Greek parish practice of censing during matins at the Great Doxology and then going directly into liturgy. This is the practice I followed during my period of serving the Serbian Orthodox Church.