I would argue that Google's account system is extremely poor.
What it considers your primary account is apparently the first one you add, so if the order is wrong, you have to sign out of all of them and start over [1].
But it's not exactly like that. Recently someone added me to a new Google Apps for Work (or whatever it's called this month) account, and now this new account is, mysteriously, the default account, even though I've had a different one for ages.
If you open Google Calendar, it will embed the account number in the URL (https://calendar.google.com/calendar/b/3/render, for example), but this number obviously isn't static. If you have multiple devices and sign in elsewhere, the number might be wrong.
You also get this number as "?authuser=3" in every Google Hangout URL. But that number is yours — when people share a link like this, the recipient typically ends up opening GH for the wrong account. Google Hangouts is notoriously finicky about accounts, and the loading screen will often hang if you happen to be using the wrong one for a particular hangout ID. Sometimes GH shows the (tiny, dark gray) account switching link, sometimes not. (Hangouts is generally a disaster when it comes to actually starting one.)
[1] http://osxdaily.com/2014/08/13/set-default-google-account-mu...