Typically this is because the remote was programmed to turn both the set top box and TV on (such as a Power on ALL button). Does your remote have an option to just power on the box and tv separately? I know my Comcast cable remote has that but not sure if that's an option for you. Essentially, the Slingbox onscreen remote should affect your home electronics the same as if you are watching tv at home, so hopefully your remote either has an option to turn on just the cable box, or can be programmed to do so.
My name is Jorge and I'm a new user, I just bought a slingbox 500 and I set it up my self, it seems to work fine but my only issue is that every time I watch slingbox on my laptop my tv turns on at home and when I'm finished watching, it doesn't turn back off, is there something I'm missing?