Some TVs will automatically find the active HDMI in-use, while others will not. If your television isn't defaulting to the correct HDMI input, you can typically tell your television, in the settings menu, which input should be the default when the TV powers on.
While all TVs differ, you will need to go into the settings of the TV and find the appropriate setting. On the TV we tested, go into Settings, then System, then Power, and finally Power On. Here you will pick which HDMI input you want the TV to default power on to. Your television may have a different menu system to do this.