In most cases, there was simply no native script to begin with. If you look at some examples of non-Latin-based scripts for native American languages (e.g. Canadian Aboriginal syllabics, Cherokee syllabary etc), they are all derived from newly introduced scripts. Mi'kmaw hieroglyphs are an interesting exception in that the glyphs themselves are indigenous, but their use as a full script was introduced from outside.

Latin-based alphabets discussed in the article have mostly been introduced in the 20th century to facilitate the revival of those languages. Although I find that Salishian languages in particular got a very lazy treatment - if you look at some of the examples in the article like "ʔaʔjɛčχʷot" or "ʔayʔaǰuθəm", that's pretty much the https://en.wikipedia.org/wiki/Americanist_phonetic_notation taken as is without much consideration for ease of use or typographic concerns (SENĆOŦEN is a notable exception to this). Kind of ironic, since many of the typographic issues the article addresses stem from this original decision.