Q. Do I need to do non-resident taxes in the other states instead of just my primary resident state?
A. Yes, but "nobody" does. See http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/ If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.
Although the article is specific to business travel, "remote work" is treated the same, since you physically worked in those states. During covid, many states adopted specific rules exempting temporary remote workers from taxation.
