It does, when it doesn't that's when you call it tamari.

Tamari is "low wheat" rather than specifically "no wheat". Many manufacturers (particularly when selling to Western markets) will simply take the extra steps to expand the market.

Eh, it depends what you mean by traditional. Ramen is "traditional" in japan, but it was invented in the early 1900s. Similarly, since wheat wasn't commonly imported into japan prior to the 1800s, most actually old tradition recipes didn't contain wheat either.