Airport extreme after linsys router not finding my synology disc/sonos system
Your AirPort Extreme will need to "control" the network in order for this setup the way you expect. The Linksys would have to be configured as a bridge with the AirPort Extreme as the router/DHCP server.

Do not that the way you have things setup currently, Time Machine will still work; however you will need to connect to the server/disk by IP address. Other features like Bonjour Sleep Proxy and Back To My Mac just won't work.