I believe that only one person can access the Slingplayer stream at a time. So, if you are using the Slingplayer remote from afar to control the TV channel that is sent through the Slingplayer to your computer, then the person at home will see that same channel on their TV.
One way to get around this limitation for the home use is to also connect a second TV signal source to your TV -- then the person sitting with the TV can change the video input displayed locally on the TV to that second source. In my case, I have an RF splitter attached to the coax cable from my wall. From the splitter, one coax cable goes to my cable box, and the other goes directly to the coax in on the TV -- this is called "Input 1" on my TV remote. Then from the cable box, a set of composite (yellow-red-white) cables go from the cable box to the input side of the SB, and a second set of composite cables go from the output side of the SB to the TV. This is called "Input 2" on my TV remote. When the TV is set to input 2, the screen displays what the cable box is receiving, and what the SB will stream. When the TV is set to input 1, the screen displays only those channels where are broadcast "in the clear" by my local TV service provider. These include the local affiliates of the large national networks, plus several other stations that make their broadcasts fully available for free. It's not the complete list of stations that the cable box receives and decrypts for my viewing, but it's better than nothing, and does allow me to watch some TV channels different from those that the user of my SB wishes to view. And when these other family members are not using the SB, then I switch to "Input 2" with the TV remote and watch the full suite of channels from the cable box.