This has absolutely nothing to do with the Slingbox. I suggest that the same thing will happen if you were in the room and turned on your Genie box with the original remote ?
There is a setting somewhere in your TV menu that tells it to switch on if it sense a signal on the HDMI cable. It goes by various names, You just need to disable it. it will be mentioned in the manual somewhere.
It sounds like the TV and cable box are connected to each other via HDMI cable. With this connection, the devices are able to control each other. This is known as CEC. The link below has a small list of some manufacturers of televisions that have CEC and what the settings is named within that television. Take a look at the link below to see if your television is listed, and if it is disable that setting on your television.
Hope this helps!
Sling Media Moderation Team