Most publishers actually specify the order to be based on alpha (author) then year and then usually title, which is what you are getting, and not in order of citation. That is because in the bibliography itself, that is how they want them to be listed.
To get around this, in my tests, you need to edit the style and change the bibliography sort order. Probably for your “esthetics” you want to sort only on “First Author” (or Author, but that will probably create some instances incompatible with your expectations), and then year and nothing else (so use the Other and specify these two fields). The third parameter will automatically be by order of appearance.And make sure the citation sort is set as the “same as bibliography”.
Save as to a new name, and use this new output style in the format bibliography options of the manuscript in question.
(note added in edit – I suppose you could make this change in the citation sort order and let the bibliography be listed in Author, Year, Title and then the letters would be out of order there, if you prefer, but I didn’t test that option.)