Have your installer mitre a piece of the nosing and add it on. This is part and parcel for vinyl purchased at a big box store. The installer has to get creative. And to be creative, you need to be good.

Vinyl was the wrong materials choice.

Unfortunately, do to certain circumstances it was the only material choice. But thank you for the helpful feedback!

Agree that is the wrong product for that application.

The installer can cut and make a return end(this example is opposite your problem, but is done the same manner). also, were I doing that job, I would install some kind of support behind that nosing, since vinyl is easily cracked/damaged. And some backing(non expanding foam or foam sheeting cut to fit) will aid in installing the return end piece.