The 1910 census shows both Friedrich and Theresa as being born in Austria-Hungary
IF Terezia was in fact born in the US she should have been able to return on a US Passport, which would have been issued in a US Embassy either in Zagreb, Croatia or Belgrade, Serbia. The manifest clearly lists her birthplace as Vukovar.
Friedrich Sr arrived 1907 aboard the Kroonland, there is a notation that he was held for a ???? exam... ancestry mis-transcribed his surname destination Sharon PA
See attachements