Yeah, when you change targets, it has to send a message to the server, which acknowledges the change. Then the server sends a message to your other clients telling them about the change. So basically, whatever your latency usually is you can roughly double that, add in a bit of extra, and that's how long it will take your targeting change to really show up.

In my case since I'm on the opposite coast from the server, I'm running at about 300-400ms latency. It usually takes somewhere between half a second and a second for the minions to pick up target changes. It's not bad once you get used to it, though. Per-character macros avoid the problem entirely when it comes to healing, and in the case of DPS I usually have a second or two anyway while spells are being cast.