You can observe it here: http://demos.telerik.com/aspnet-ajax/rotator/examples/carouselmode/defaultcs.aspx by clicking either of the sequences. Note: set the rotator to CarouselButtons to avoid cinfusion stemming from automatic advance.
- red, grey, green. You will see red instead of green
- blue, green, gray. You will see blue instead of gray
One more item was rotated in each case.

A workaround is to disable animations for these second and last items when their counterpart is currently shown:
function OnClientItemClicked(sender, args) {
	var shouldAnimate = true;
	var indextToChangeTo = args.get_item().get_index();
	var currIndex = sender.get_currentItemIndex();
	var itemsCount = sender.get_items().length;
	if (currIndex == itemsCount - 1 && indextToChangeTo == 1 || //last item is shown, the second item is clicked
		currIndex == 1 && indextToChangeTo == itemsCount - 1) { //second item is shown, last item is clicked
		shouldAnimate = false;
	}
	sender.set_currentItemIndex(indextToChangeTo, shouldAnimate);
}