You have to manually import the tracks in both the client on your home computer and in the client on your phone. Spotify doesn't provide any upload / cloud functionality.

No, that's not correct.

I have loaded several track to Spotify on my PC, and can listen to them using the client on my phone without having to manually load/import them there. They sync automatically when you connect.

Is your computer running when this sync happens or is it uploading to the cloud?