On P57 of the ACKS core rules is a table that shows the advancement for all classes that appear in that ruleset in terms of gaining new proficiencies.
I cannot find the equivalent table for the new classes in the Players Companion.
There’s a mention of proficiencies on P81 of the PC, but not in the context of advancement only in terms of the list of proficiencies available when building custom classes (though I note there’s no mention of proficiencies in the Custom Racial Classes section)
I believe that everybody gets a General proficiency at 1, 5, 9 and (if they make it that far) 13.
Everybody gets a Class proficiency at 1, but then only get another when their throws roll over. Mages’ throws advance by two points every six levels, so they get new class proficiencies at 6 and 12. Fighters advance two points every 3 levels, so they get new Class proficiencies at 3, 6, 9 and 12. And so on.