You wont get invaded when you are not at home, or any base but the longer you are in a area that has a campfire + bench + bed will increase the chance to trigger an invasion.
The different invasions are controlled by bosses killed and mobs killed, like when you kill the 1st boss you get greys, if you take out a troll you could trigger troll events and when you kill the 2nd you could trigger swamp events.
Some events trigger in a specific area like wolves in the mountains even without the usual equipment, its a you are in a specific area trigger.

Event mobs invading your bases have a spawn circle and the mobs will try spawn at the edges, but limiting the space may make them spawn closer, or underwater.