The power button on the remote is only for the TV. Roku devices never really turn off. Some have a "power saving" option under Settings->System->Power which, if enabled, will put the device in a "sleep" state. You can wake the device by pushing any non-TV control button. I'd suggest pressing Home a few times after you turn on the TV.
Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution."
If you appreciate my answer, maybe give me a Kudo.
I am not a Roku employee.