St. Joseph's Orphan Asylum was at least at one time, if not for it's duration, a part of the Pontifical College Josephinum: see http://www.pcj.edu/aboutus/history.html and http://www.pcj.edu/journal/history.htm

Their home page further clarifies:
"Founded in 1888, by a German immigrant priest, Msgr. Joseph Jessing, the Pontifical College Josephinum was granted pontifical status in 1892 by Pope Leo XIII, thus becoming, and remaining, the only pontifical seminary in the Western Hemisphere.

Originally founded by Msgr. Jessing, in 1875, as an orphanage, today it educates seminarians from the United States, Asia, Africa and Europe."

I've emailed the Josephinum's Archivist for more information. I'll post information I receive from him here.

Rick.