My ancestor Willm Jacobs Tammen b. 17 FEb 1850, Eversmeer Ostfriesland Germany, arrived in America at Galveston, TX in Oct 1890. with his wife Hauke Wina Decker Tammen and six children. They took a train to Wichita Falls and live there the rest of their life. The 'family' story is that they arrived at New York on 'the big boat' and transferred to a 'cattle boat' for the trip to Galveston. I have searched all the records of Castle Garden in New York and have not found them also the Galveston Ships lists do not mention them. I would like to find what ship (s) they traveled on and the dates they arrived in New York and Galveston. Or when and where they left in Germany. I feel that I will have to find a record on the German side. Where do I go from here.
MY ANSWER: Yvonne, it sounds like you have done a lot of research and kept track of the family lore. One thing to make note of is that the Galveston Ships Passenger Lists don't include passengers who transferred en route. So that means if your Tammen family came in to any other port first, then on to Galveston Texas, they will not be on the incoming Galveston Manifest.
You would have to look for them in the main port they arrived at. If your family story is of a New York arrival, you may want to search there first. You can always expand your search to other ports of arrival if you need to. You mention checking Castle Garden records. It's important to note that Castle Garden existed as a processing station for immigrants between 1 August 1855 and 18 April 1890. So after 18th April, it was no longer Castle Garden.
Passenger lists for the Castle Garden time period (and beyond) are available on microfilm and online at Ancestry.com
Another point to mention is that there are a few problems with some of the New York passenger lists. In general from about June 15th 1897 until March or April 1903, the lists for first class and second class passengers were not collected at Ellis Island
and do not survive, so therefore will not appear on microfilm, nor in the Ellis Island online database. I know this may be too late for your Tammen family arrival but it's something to keep in mind. Marian Smith has written several articles on the Missing Manifest problem on her blog
Was your ancestor naturalized? The 1900, 1910 ,1920 and 1930 census identify citizenship status, with notations showing the individual was an Alien, or had started the Naturalization process or had his final papers. I see that in the 1900 census he had his first papers (PA in the column for citizenship details) so you can have a hunt for those. If you check 1910 it will tell if he is naturalized by then. You can read more about the value of census records in your search for an immigrant ancestor on the website NaturalizationRecords.com
Last but not least, you could research all the children. Since they were all born in Germany there is a chance that an obituary might provide more details on their immigration to America.
I'm also curious what your source is for the arrival date you gave of October 1890. Depending on the accuracy of the source, the date may not be correct. For example if you found this date on a census record, you cannot trust it to be correct. Immigration and Naturalization years are often mis-remembered so you should always search a year or two on either side. I saw that in the 1900 census, Willm has a date of immigration of 1890 but you should be searching in a wider range unless you have other evidence showing that year.
If you want to respond to my answer, please post it as a comment here on the blog and I'll try to help further if possible