Terms/Tags aren’t ordered.
To help make the terms easier to read, the editor will list them alphabetically, but that isn’t because they’re ordered alphabetically in the database. It’s because a piece of javascript sorted the terms in the UI control.
There is no order, only the order you give them. Fundamentally terms have no order. Any order you see in the editor is purely circumstantial, there is no order mechanism in the database for terms.
If you want to give special meaning to a term, you need to do so explicitly, e.g. store the term ID of the significant term in post meta. You cannot rely on order, as terms do not have order.