Timeless seems to sort all categories alphabetically, which can lead to a strange order: E.g. https://en.wikipedia.org/wiki/2018_FIFA_World_Cup?useskin=timeless has the "July" categories before the "June" one. They should be kept in the order in which they are in source code.
Off the top of my head the only reason I can think of why they'd be sorted alphabetically to begin with (because as you say, the on-page order is indeed more logical) is probably because they're actually being pulled straight from the database or something similarly idiotic because there's just no built-in way to get them... not entirely pre-rendered as html? Even so, if it normally gets them in the proper order, there must be some way to replicate the behaviour...
Needless to say this needs looking into.