Welcome to Sling Media's online forums! To answer your question, you will have to watch what is being viewed on the set top box your Slingbox is connected to and if you do change a channel, it will change at home as well. However, there are some steps that can be done to bypass this issue. some customers will get a designated set top box for there Slingbox alone and some cable and satellite providers have what is called a dual tuner set top box. Below, is a link to look into this issue a little further.
I hope this helps, if not please reply with any other questions you might have.
Sling Moderation Team