I do not know if Science has a convention for this, but let me tell you about the convention in Economics and Finance journals. The most common way to reference articles is to cite by authors-date and in alphabetical order, for instance: Kahneman and Tversky (1979). In Economics or Finance, the order of the authors does not usually indicate any seniority or importance in the contributions.
If the non-alphabetical order of authorship indicated anything, the authors would usually explain it in a footnote. For instance, I have seen authors indicate that the order reflected the winner of a particular game of chess, but I do not recall which article it was.
Authors who publish quite a bit together occasionally swap the order of the authors, e.g. Tversky and Kahneman (1991). This can be done for a variety of reasons and it is up to the authors to decide to do that. The journals would not (as far as I know) make any such request. A common reason for non-alphabetical listing of authors is that the authors have two papers published together in the same year and they find it clearer to use the reference style Tversky and Kahneman (1991) rather than Kahneman and Tversky (1991b).
Examples of References:
Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
Tversky, Amos, and Daniel Kahneman. 1991.
"Loss Aversion in Riskless Choice: A Reference-dependent Model". The Quarterly Journal of Economics 106 (4). Oxford University Press: 1039–61.