Split your emails using Gmail priority inbox
After playing with the Gmail app, I realized that they missed one detail in the link that you posted. Here's what you're supposed to do:

After switching to priority inbox following the instructions in the link, you have to then manually switch from the regular inbox, to the primary one. To do that, open the menu, and press on priority as shown below. After you do that, it will open it by default unless you switch back.