You have to be outside their perception range which is ~30 meters (but varies for some creatures and bosses)
https://valheim.fandom.com/wiki/Creature_senses

I believe there might also be random spawns based on progression. I've been in the middle of a rather large black forest and encountered a lone fuling.

I believe that raid 'leftovers' who don't get killed during an event, do remain spawned and create havoc in the biomes until they die, since biome vs biome is happening...causing "out of biome" NPCs. I see fulings all the time in the neighboring Mistlands biome and Black Forest NPCs there as well, it's at an intersection of 3 biomes.

My observation: during a Night 2 Day cycle, the night spawns disappear when dawn arrives, while after you get the prompt for an event ending.....they do not 'poof'/despawn out of existence/instancing.

czekam kiedy nowy the forest wyjdzie odrazu zakupiam

Critters will run a long way into another biome and be there days later creating havoc. Nowhere is safe, especially near the Plains. Keep your sound turned up as the gigglers and buzzers always announce their presence, always. Well, almost always.

Noisy activities seem to attract the mobs, so I try to be well away from a border biome before chopping wood or mining. I don't know how far it is but it seems larger than their visual range.

Fighting a 1* seeker in the black forest is always fun!