Before I post I am gonna state that I am in no way trying to advertise another server. I'm trying to get help and advice. This is happening on my sister's private multiplayer server when she and I are in it. She says she tried to get help from Minecraft Forums but they told her the only way it would be happening was if she placed a bunch of spawners or spawned them herself. She downloaded a pre-made map of floating islands so we could have something different. She says the server is set to peaceful but yet mobs spawn like crazy. I found a spot with so many mobs we were lagging and she swore I spawned them all with eggs. Yesterday she loaded it back up and there were mobs like crazy once again. They caught fire during daylight and burned down her tree and tree house. She then went to a spot with nothing but void and built her own island and lit it up and I added torches but mobs spawn like crazy as well. We clear it off, turn around and there are mobs popping up again.
So it's a custom map?. Try with a normal map. If it still happends stop the server, set the server to peaceful in the text file. Start it back up. That should help,.