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Quite a few cable boxes have a type of power save mode that will only allow for the cablebox to be on if the TV is as well, this way when there is no one at home watching, it can help you to save power in the long run.
You should be able to go into the menu of your Set Top Box and disable this setting, which should resolve the issue.
I hope this helps!!!
Sling Media Moderation Team
While that may be the case I think it is more likely that your TV has a setting that turns it on if it senses a video signal on the HDMI input. And that is happening when you remotely turn on the DVR. In fact this has nothing to do with the Slingbox, it will probably do the same if you were at home and turned it on with the real remote. Go into the TV settings and disable it.