Yes, Tulugaq is still standing in the Rat Swarm's swarm aura. So "Surrounding rats" was mainly a descriptive way of conveying that your are being gnawed upon by the swarm aura. The way I envision most swarms is that their bulk may reside in the square they take up but many more make up the "aura" they project.
The swarm aura is designated by the large slightly transparent red circle. If you are in the red then you will be taking 4 damage at the start of your turn each round.
Incidentally, the larger black circle also represents Galadren's bat swarm from his daily power. Every creature in that area of effect is in difficult terrain, based on the powers description.