I wasn't aware of a specific "expatriate" legal definition for immigration. Refugee/asylum seekers is a category, certainly. "Artist" is another. "Self-employed" is a third. "Because of family connections" a fourth. "Au pair", "athletic coach", and "retired" are three more. Certainly "people who work for temporary periods as a specialist employee of an international company" is a category, but that's not the only way to be an ex-pat.

Consider Arthur C Clark. I believe you would consider him an immigrant. He specifically chose Sri Lanka (then Ceylon) because of its reefs (and likely other reason, but that's his main stated reason). But by all accounts, he was a British ex-pat in Sri Lanka. He was even recognized by the British royalty for his cultural services as a British person.

Since so many people consider him an ex-pat, and your definition doesn't, I suspect your definition isn't all that useful even in your informal sense.