To clarify, for a reemergence to happen, there first must be a rebellion/uprising (less than 100% happiness). If the province was previously owned by a dead faction, and the game is tracking a potential leader of that faction (an underage heir when the faction was eliminated, so up to around 60-80 years from the factions demise), the rebellion/uprising becomes a reemergence. Now, all the provinces previously owned by the faction are checked, if the happiness ratings are below 120%, they can become part of the reemergence.

So to prevent your own provinces from being affected, you need to keep your happiness above 120%. This will not prevent reemergences in provinces owned by other factions, but it will keep your lands from getting sucked into them. If there are no rebel provinces, and everyone keeps their happiness above 100%, a reemergence will not occur since a rebellion/uprising will not occur, but this is a pleasant fantasy scenario in Total War.