I think the only way it will work is if you connect via Bluetooth(if the echo dot can do that). Casting basically just sends a URL to the device and it fetches the audio feed itself. Since xmanager isn’t on the echo, it can’t block the ads.
I have the same issue when playing through my Google Home’s. I tried looking for a domain to block through my router, but I couldn’t find one that wouldn’t also block the music.