It could be the case that all fonts contained in an AI file are indeed loaded on neoStampa, but when opening on neoStampa a PDF exported on Illustrator from the same AI file, some fonts look replaced.
The following image is a screenshot of a neoStampa job output (it also looks like this on the job preview). All the AI fonts are fine, whereas most of the PDF fonts have been replaced by a single one.
When it comes to load the content of an AI file, neoStampa loads the PDF data contained in the AI. On the other hand, it does not have the capability to replace fonts that are missing in the system. So, since neoStampa does not manage fonts, the font replacement had to be carried out on Illustrator.
This is how the situation was caused. The Illustrator user that made the AI document had all the fonts. This user shared the document with a second user that had only a few of them. Then, the second user exported the document as PDF and replaced the missing fonts at export by clicking on "Yes" in the replace-font dialog on Illustrator.
This is quite easy to check on any Preview application. Just open both files and see the fonts are shown the same way as neoStampa did.