I had this exact same learning experience. Only, it took me running out of propane entirely
twice before I learned how this works!
Learn To RV: Understanding my Automatic Propane Changeover
Basically, yes - it will automatically switch over from the first to the second.
You should leave both tanks open.
There is a glow dot/light-sort of thing on the automatic changeover that tells you the amount of propane in the one that it's pointing to. Once that shows you it's empty (internally it has switched to the other one), you can switch the pointer to the 2nd tank and it'll tell you full vs. empty on that one. You can disconnect and take the first/empty one to get filled.
You have to check your propane changeover on a fairly regular basis until you get a feel for how often you go through propane.