I'm currently reading John Man's "Marco Polo", a combination history/travelogue.
He notes that the Mongolian word tumen and the Chinese word wan both mean 10,000 and are also synonyms for "lots", or "big number".
Since in places the records note 2,000 or 3,000, then it follows that tumen means substantially more than that but not necessarily 10,000. So a Mongol force of 3 tumens may well be less than 30,00, even before any losses.
The book has a blurb saying it is "the history behind the Netflix original series". I guess what little history (names of the characters, etc.) is in the series came from this book. I could do with more history and less travelogue but the author seems to know his history and languages.