The distinction between emigrate and immigrate is more a matter of where the sentence is placing its attention.

In cases where both the from X and to Y clauses are in the sentence, you might then need another rule for which one to pick, if you're only going to pick one. I note that even here, in your example, the rule apply - emmigrate from, and immigrate to.

If you would specify both emigrate and immigrate, it will be "emigrate from A and immigrate to B" and "immigrate to B and emigrate from A", again, consistent with the rule.

Do you have an example where my proposed usage would be mistaken?