They are a Society of Apostolic Life. I attended their celebration Mass at Notre Dame Cathedral when this happened. As such, they still report to the Bishop and get their assignments from him.
Incidentally, His Grace Arshbishop Terrence Prendergast has, as of yesterday, assigned Companions to two new Parishes in Ottawa. They now are in:
- St. Mary’s (their home base).
- Holy Redeemer.
- St. Maurice.
- Blessed Sacrament (new).
- Annunciation of the Lord (new).
Anyway, I’ve been in Ottawa for several years and know SEVERAL Companion’s of the Cross. As mentioned they are VERY orthodox. Also notable that they have one of the very few officially fully BLIND priests. Father Tim uses his memory and braille to do the Mass parts (in an incredibly funny moment, he once said during a homily that to highlight his Bible he’d have to use something sticky over the braille so it would stand out from the other bumps!).
They’re also charismatic (think Steubinville, if you’ve ever gone). So if you’re not a fan of that, they might not be for you. But if you’re into the Charismatic renewal and want orthodoxy, head to the Companions. If you want more traditional and still orthodox, you hit up the FSSP.
If you have questions about them, let me know. I’m not kidding when I say I know a large number of their priests, and know a lot about the order.