If rumination does fit into this, I think the cue is considerably more general than that. At least for me, it seems more like it's triggered internally, by my thoughts turning to a particular subject (probably combined with an emotional state), than by any external cue. (I recently had rumination triggered just by being reminded of the word "rumination" and thinking "oh yes, that's the name for the thing I've been doing...")

But it's not obvious to me that we'd expect rumination would fit into this. I don't think fear is a habit, for example, even though it has a cue, a routine and a reward.