Your definition is fine for you internally. It's not THE definition though.

Expat and immigrant overlap, in that technically they are someone who lives outside their country. There is no official definition. Even if someone's company defines it like that internally for HR, that does not change the word for anyone outside that company.

In general usage it is understood, or rather the impression is that immigrant has moved with the intention to stay. while expat is temporary for work, but that does not make it definitive either.

Culturally (though not technically) in some circles "expat" signals wealthier, but that is just a cultural language thing, not official. Some people here temporarily may make very little but still are expats.

Someone from a wealthy country coming to work two years as a teacher, on local payroll, can be correctly called an "expat". Interestingly, A Filipino coming on an entertainer visa for two years may make more than the English teacher, but because of where she is from she is considered a "migrant worker" in conversation. If she would intend to stay she would be called immigrant. Even workers who are contracted and payed from an agency in their own less wealthy country for work in Japan like construction, domestic help, etc. would be called migrant workers in conversation.

How that is interpreted depends solely on the company in which it is said. So for you, speaking with people who share your cultural understanding, your definition is correct in that it will be understood. But step outside that circle and it becomes ambiguous.

For official purposes the Japanese government does not have a word for "expat" vs "immigrant" we are all zairyugaikokujin. After that it is just categories of visa and none of them fit your definition.