When I say "Hey Google, play Spotify on <Chromecast name here>" to my Google Home, it starts Spotify on the Chromecast in a different mode than if I were to start it from either my Android or iOS device, and this results in the inability to control the volume from the Spotify phone apps. Let me walk through the successful use-cases, and then describe exactly what happens when it fails.
If I cast to the Chromecast connected to my TV (for example) from Spotify on my Android or iOS device, I can then control the volume of the music on the TV from within the Spotify app. This is true regardless of which device started the cast; both devices have volume control no matter which one initiated the cast. This is all fine and good.
If I cast to that same TV from my Google Home, by saying "Hey Google, play Spotify on TV", Spotify does indeed start playing on the TV, and it even picks up where I was in my current song. It also lets me use the play/pause/skip buttons on any of my devices, and respects the play queue. This is lovely. However, for some reason, it does NOT let me control the volume from the Spotify app on Android or iOS. The volume slider simply doesn't show up in the Devices menu. The volume buttons also do not control Spotify's volume on the TV, instead they stay controlling the volume on the Android or iOS device itself. It also does a weird thing where it shows that I am casting to the TV (by saying "Listening on TV" in green letters in the devices menu), but it also has a second TV entry, that says I can cast again to the TV. If I tap on that entry, the TV goes black, the Spotify app on the Chromecast appears to restart, and then everything works as normal. This does interrupt the music, of course.
This issue happens every time, on Android or iOS devices, when I'm casting from the Google Home to any Chromecast audio, Chromecast video, Chromecast Ultra, group of Chromecast audio devices, or even the Google Home itself. It's both puzzling and obnoxious. I'm not sure what the Google Home is doing when it's launching the Spotify app on the Chromecasts that's different from how it's launched when you do it from Android or iOS, but it's pretty clearly an unintended bug.
Thanks for reporting this. We can confirm the tech team are aware of the issue.
We don't have a timeframe for a fix, but hopefully we'll have an update soon.
For now, we'd recommend keeping your apps up-to-date.