The term "person first" was something obviously created thinking only about English, where adjectives come before a noun but adjunct prepositional phrases come after it. Cross-linguistically that's uncommon, most languages are more consistent (or more flexible) on the placement of noun modifiers relative to the noun.
In a strongly head-final you'd expect anything that modifies a noun must go before it, regardless of the wording, while in a strongly head initial language the modifier goes after it. So describing any term as "person-first" in a language like this doesn't really make any sense.
However the (assumed) meaning is less about the word order and more about the perceived difference in the relationship between the noun and modifier. But I have no idea the fact that English uses differencing word orders for different modifiers makes English speakers perceive more of a difference between the constructions.
You also have to consider that in many languages only one possible construction might exist for both of the English ones, which I'd assume would render the debate moot.