The solution of the issue is to increase the default _requestDelay time of the control which will allow sending the request with the correct searching data according to the custom scenario. Here is a sample code how to achieve this:
 function pageLoad() {
                var au = $find("<%=RadAutoCompleteBox1.ClientID %>");
                au._requestDelay = 500;
            }
From the upcoming Service Pack we have added public get_requestDelay and set_requestDelay for this setting of the control.