Flooring installer left the side by the staircase unfinished. Should he have installed nosing first? How can this be fixed?

Nosing is a good trim for steps. Maybe the trim carpenter has a better idea...
Do you have a picture to show?

A rail shoe can be installed with an edge strip, without nosing. The balusters will be separated by fillet between each one, instead of the balusters being dowelled into place after a nosing has been installed. This ought to have been determined on the floor installation contract.
Nosing can be installed by ripping along the edge of the floor anytime if it is available. Sometimes the nosing needs to be finished to match the finish of the floor by the floor mechanic.