I would suspect the Jesuits are not under Dolan’s direct control, being an order among themselves and having their own “Black Pope” leader as he is called. I know the Jesuits in Milwaukee were not when he was Archbishop.
You are quite correct. Neither the parish nor the high school of St. Francis Xavier come under the authority of Cardinal Dolan. They are under the authority of the Jesuit Province of NY State.I would assume the same for St. Francis of Assisi on 32nd Street. They would fall under the authority of the Franciscan Friars Minor. Xavier has for a long time been very welcoming of the homosexual community. My brother in law and his partner when they would have the family for Christmas Eve would attend services there as they lived about a half mile away. Even though I am a graduate of Xavier HS my wife and daughter and I would attend services at Epiphany parish on 2nd Avenue instead.
Whether or not Dolan is the Jesuits’ direct ecclesiastical superior, he still has the duty to preach and teach as well as set up direct public confrontations (”teachable moments”) if he wanted to. It’s not like he’s some little 12 year old soprano in the Schola Cantorum at Holy Innocents.
The Cardinal Archbishop of New York is not without the means to convey his desires and to give them weight.