I've faced The Goblin Army and The Pirates a few times now. But the most recent time I faced them, I noticed that they only appear to be in the centre of world. I was in the Crimson farming for a key mold, and thought the invasion would help to get it.
When I spawned the Pirates, a few came but no more seemed to spawn. Later on when I went back home, there they where. I fought them and defeated them. The exact same thing happened with The Goblin Army.
So do they just spawn in the centre of world, or was I just doing something wrong?
Best Answer
When you first summon the Pirate or Goblin invasion, the message appears saying:
The initial wave of enemies enter from the edge of the world, the direction is specified in the message. These enemies will then begin to move towards the middle of the world.
When the following message appears:
This means that enemies will begin spawning in the middle of the world.
Hence, only the initial wave of Goblins/Pirates spawn away from the centre of the map, the rest of them spawn in the centre of the world only.
Wiki pages for reference: