The Issue (Appears to be active on latest Spigot version):
The issue appears to not be resolved as marked on previews issues. I've tried posting on issue #5156 on 16/Jul but so far no answers. I'm creating this new issue because I've had to prohibit players from going near Pillager Outposts because it would spawn non-stop until the server is completely lagged.

Below are links to the world downloads where one is running on Vanilla Server, and the other on Spigot - note that both are the same map just different server.jar. The one running on Vanilla is working as intended where Pillagers are spawning and despawning without issues and not causing an overflow. The one running on Spigot is spawning Pillagers but they don't despawn.

Now I could be wrong, but the issue appears to be that they're not despawning. Almost as if the game tries to despawn them but doesn't removes them from the server, and then spawns in more pillagers because it thinks it just despawned a few and the cap is not full. Again, I could be wrong.

Coordinates for Pillager Outpost where the issue is happening is:
X: -7672
Y: 208
Z: -478

World downloads: 
[World running on Vanilla|http://www.craftera.com.br/downloads/worlds/season1/vanilla.zip]
[World running on Spigot|http://www.craftera.com.br/downloads/worlds/season1/spigot.zip]

Steps to reproduce:
1) Download Spigot world from link above;
2) Teleport yourself to the coordinates above using the command "/tp -7672 208 -478";
3) Set render distance to 20 or something;
4) Go to the edge of the platform that you've just teleported yourself to, look down and wait there for a few minutes watching the Pillagers spawn non-stop (directly down) without despawning.

Duplicates marked as resolved (I don't know why):
https://hub.spigotmc.org/jira/browse/SPIGOT-5009
https://hub.spigotmc.org/jira/browse/SPIGOT-5156