Project tempo

I just stumbled upon this problem. I changed the tempo to a multitrack session from the Preferences > Time Display. I closed the session and opened another older session, but the playback wasn't right, a bit too slow with a weird delay. I finally figured out it was the tempo change I had made for the other project. 

So am I missing something or is the tempo always a global value for every session you have open at the same time and you have to manually set it from the preferences every time you switch between projects and the tempo won't be saved to the project file? This seems very counterintuitive to me.