This 'casting' option is built into the Netflix mobile app. See more here: https://help.netflix.com/en/node/49?ba=SwiftypeResultClick&q=mobile%20app%20
I'd recommend trying to remove the Netflix app from your phone, restart it, then reinstall the mobile app and try once more.
If you're still experiencing an issue with the Netflix mobile app automatically casting to your Roku device after trying the steps above, we'd recommend contacting Netflix support to report the issue and request additional assistance.
Roku Community Manager