Different volumes streaming Spotify

That is because each recording is made at different volume levels and different amounts of compression.  You are not doing anything wrong. 

The ideal case is Spotify modify their app so when you play a song at a volume level you like, it remembers the setting and auto adjusts at the start.    But that is just wishful thinking, which is one step below making recordings without any compression.   Sigh.....   

I think there is a setting in Spotify to "normalize" all the tracks in a playlist. But if you are not using playlist, but selecting songs from different albums, then it will not work.

Normalize.  
Ditto

Yep, normalize. Technically, it degrades the sound somewhat, but it’s Spotify, non issue.

I try a Spotify downloader to stream Spotify on my iPhone offline without any problem.