Disconnection problem

When I disconnect from any server it tells me that I'm already logged in, in other words it delays my disconnection, so when I disconnect it delays it and keeps me reconnected for about 10-15 seconds before I can rejoin. I tried disconnecting from different PCs but still the problem is there. I don't know what to do but in conclusion I think it's a Internet problem as I tried with other computers in my home, but this is a really big problem as it gives an disadvantage, for when I disconnect it keeps me reconnected which allows players to hit me although I disconnected. Please help!