Hi Lillian,
I got some help from AJ Kauffman, who showed me where to look for the API code that applies the Templates.
From what I can tell, the BC API page inserts the record first, and then the API Setup code is run to apply the template to update the inserted record. Because the Item is inserted before the Template is applied, it defaults to using the No. Series from the Inventory Setup page.

I am not yet able to decipher the actual template field update code, but my guess is that API Setup does not attempt to use the No. Series from the Template because that would require that it modify (renumber) the existing Item No. value for the new item record.
If my understanding is correct, I can guess why this limitation exists. Presumably re-numbering an existing record is a more involved process.
But on the other hand, that is unfortunate, as I can imagine lots of scenarios where one might want to use different number series for imported records, whether those are items, customers, vendors, sales orders, etc.
I'm now wondering if it is possible to create a custom API that will lookup the Template, retrieve the next number from the No. Series, and assign it to the Item during the API call. Likely possible, but it would be custom.