Is there a difference if you use different buttons on the Roku remote to switch to its input (e.g. pressing Home or play or back)?
If you use the TV's remote to switch inputs, does the The Roku Channel open?
1) When you use the Roku remote to switch inputs, Its possible that the screensaver you are using has show or app ads that load the app for the show when you press play on the Roku remote - try changing the screensaver:
Setting/Theme/Screensavers/Roku digital clock/Set as screensaver
2) It's possible your TV's remote is sending an additional IR signal when used to switch inputs causing The Roku Channel to open - try covering up the front of the Roku to see if this is the case.