Your target was traveling with Ludwiga Tonkowicz to Ludwiga's brother Jakob (and Aniela's cousin) in New Bedford, MA.
As was usual at the time, an unmarried woman arriving alone was expected to have a male member of the family -- or an intended spouse -- meet her at Ellis Island. From Ludwiga's entry, it would appear that her brother was not there to meet them and a call had to be made. They were detained while this occurred. The date and time entries would support the contention that they were not examined until the late afternoon of 30 March. This may be the reason that they were noted as "too late" for Jakob to have gotten to NY on that date.
The meal count would seem to support that they received supper on the 30th and breakfast on the 31st. They were released on the 31st to continue on to their destination (Dest.) which was New Bedford.