All Kingdoms campaigns run off the same kingdoms.exe so all can use elements from each other.
In Kingdoms factions can re-emerge either with armies or in settlements. If you want them to appear like the Mongols with preset armies at given times it's recommended you use spawned_on_event. The Baron's Alliance uses the shadowing and shadowed_by parameters first introduced for Roman Rebels in BI, and I believe the faction_emerge scripting command is simply the realization in scripting of what was hardcoded for those two BI factions.
For the event method you use spawned_on_event in the descr_sm_factions entry. You also need dead_until_resurrected on a new line in the descr_strat after ai_label for that faction.
Code:
faction timurids, spawned_on_event
Code:
faction timurids, balanced smith
ai_label default
dead_until_resurrected
denari 10000
denari_kings_purse 3000
For the 'faction_emerge' scripting method you use shadowed_by for the faction who it spawns from and shadowing for the faction which will spawn. You further use dead_until_emerged and re_emergent in the descr_strat faction entry.
Code:
faction england, shadowed_by barons_alliance
faction barons_alliance, shadowing england
Code:
faction barons_alliance, balanced smith
ai_label barons_alliance
dead_until_emerged
re_emergent
denari 15000
denari_kings_purse 3000
There's a third method which I haven't explored that is used in BI and is still available in Kingdoms. That is the following.
Code:
faction goths, spawns_on_revolt ostrogoths
faction ostrogoths, spawned_by goths
Code:
faction ostrogoths, balanced henry
dead_until_resurrected
re_emergent
denari 10000
It's been a while since I've played BI, much less that particular campaign, but I imagine it's pretty straightforward and whenever the goths have a province revolt, it goes to the ostrogoths rather than the slave faction.