Here's a snap of my profile when I select it from the top of the left-hand drawer menu:
How does the app decide which three profiles of mine to show in that view? It makes sense to show MSE and SFF, because those are the sites where I have the most rep. But the app is not choosing my top three profiles by rep, otherwise Stack Overflow would be nowhere to be seen - it's 25th on my list at time of writing.
When you look at someone else's profile in the app, the first expanded line is their profile from the site you're currently on. After that, it displays the top two sites by rep (not including the one that's already been shown).
It seems that viewing my profile from the sidebar is behaving the same way, but in the absence of a "site you came from" to show first, the app is just choosing Stack Overflow. Instead, it should just show my top three sites in rep order.