Hi Eric, I use both Ancestry.com and http://stevemorse.org/http://stevemorse.org/ to search the Ellis Island arrivals. Tekla and the children’s May 10, 1906 Ellis Island record is indexed differently on both sites: Ellis Island is indexed as “Tettla Miszczsyza”. Ancestry.com is indexed as Tekla “Miszezeyya”.
Joseph’s January 30, 1905 Ellis Island arrival record is indexed the same on both the Ellis Island site and Ancestry.com as “Jozsef “ Miszczyszyn.
As to your question about Joseph’s immigration, yes, he could have had a couple of passages to the U.S.One in 1903 (if you believe the census records) and another in 1905.