An Apostolic Administration is not a group or a religious society or congregation, but is a normal and official ecclesiastical circumscription of the Catholic Church, the same as a Diocese or a Prelature or an Ordinariat, that is, a particular church, part of the Universal and unique Catholic Church. Because of that the Bishop of the Apostolic Administration has the same power as an diocesan bishop, in his jurisdiction.
As a group of traditionalist Catholics thus fully within the Roman Catholic Church, they recognize the authority of the Pope as Vicar of Christ and Shepherd of the Church, the legitimacy of the Second Vatican Council, and the validity of the Mass approved by Pope Paul VI. The Priests of the Apostolic Administration have the faculty to celebrate in Latin the Mass and all the other sacramental rites in the form codified by Pope Pius V and modified by his successors down to Pope John XXIII.
More information can be found at the Apostolic Administration's website, here (Portuguese language).