DNS Round Robin

If I need to implement a round robin example for Terminal servers or web servers.
In DNS I will have to put the same A record name with different IP address for each server, and make sure the round robin option is checked in DNS.

let s say the A record name for Terminal servers is TSFarm and web servers is WebFarm
After all this done, I wonder when a user connects to one server in the farm then disconnects, then connects back  if a different server will be connected to or the same server that the user disconnected from will be connected to.
I know it seamless to the end user, but if the client caches the IP of the previous connection, it will be used in every connection, and this will not help the purpose of using round robin.

So how do you configuring round robin, in order to rotate between the servers?

Thanks