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The impression I got was that playing actively in the opening meant there were opportunities for relatively large gains in sharp unsettled positions. The opposite was a sort of slow, grind-it-out type of game hoping for an accumulation of many small advantages.
In TheMasterOfHaengma, "active" is used to describe positive results. It is applied to both white and black. Rather than komi, it seem to stem from the need to use sente to achieve more than simply fixing shape, the need to create initiative rather than lose it. For example, if one side can resolve/settle the position and then play the next important point (a sort of tedomari not necessarily a tenuki), then the book would say the result is active, hence good.
So I presume it originates from overcoming the last move, or on the first move, Black overcoming komi. (Being always half a move behind)