You may be searching the right way however it was probably too early to obtain the information you want from those records. According to this Ellis Island link about researching U.S. immigration records, it seems:
The person's birthplace was not requested on ships' lists until 1906."
This was common, and most passenger lists had very little or no information, but you never know. My ggrandmother came to the US, alone, at age 11, in 1858 - very much before 1906 - and her passenger list had her place of birth. Since I had her parents' names from her death record, I ordered the bmd from LDS for that town (luckily they had the right years). And despite the fact that she had a very common name (Sara Hirsch) and the passenger list said she was 8 years old, her parents were right and her birth date was right. Later I found that her sister came also, in 1870 - also before 1906, and also with the same birth place.
The bottom line is that you never know until you find the record.