My pc and my mobile are using the same wireless router. But I am able to use 2 networks. 1 of my time capsule and 1 of upc but i am using the one of my timecapsule on both devices. Is that what you mean?
Yes, both need to be connected to the same network, so that's fine. The only thing left then, assuming you turned off any software firewalls, security and antivirus apps, is that the time capsule is stopping the phone from showing up on spotify on the PC. I don't know enough about the time capsule to offer any suggestions but maybe someone else has experience.
I did notice people complaining that the lack of UPnP on the time capsule stopped various other apps working for them.