First lets start with what sources do you have connected to your slingbox pro HD unit; and how are they conencted (what cable set ot input is each assigned to).
*The internal tuner only works foroff air channels from OTA or cable channels from providers that do NOT require the use of a descrambler set top box in order to decode their stations.
The way you would conenct cable for example would be as follows:
Cable line from the wall into the input of a 2 way spitter. One of the outputs of the 2 way splitter into the coaxial input on the slingbox. the other output of the 2 way splitter gets connected to your existing cablebox or tv's coaxial input.
When you select the coaxial input on the slingbox form the input list in either the desktop slingplayer application, your cell phones application or the web portal viewer, you can independantly change channels and view content without effecting the locally connected tv viewer. HOWEVER as I mentioned, this only applies to the above referanced senarrio indicated with the *.