I've tried everyday for a week, and so far Running has been unable to detect my tempo. I've tried to make extra sure that I was running at a constant speed. I've tried rebooting the phone. I've tried uninstalling and then reinstalling Spotify. I even did a full reset of my phone (although I did restore my data from iCloud).
I got it to work last night. It seems I wasn't running fast enough for it to pick up my tempo! I'm not too impressed though. The tempo it guessed was way out (too fast!) and the music was very bland, background music. Maybe that's what people want but I think I'd rather pick my own music. I also thought that the tempo would change if you sped up or slowed down but it doesn't.
If there was an option to 'turn off' or not show the running feature I think that would be good, it would make the app less cluttered.