By default, if you have both the Pushbullet desktop app and the Pushbullet browser extension installed, then Pushbullet notifications will only show in the desktop app, with no option to have them show in the browser.
I raised this issue on reddit, but unfortunately the Pushbullet devs were against implementing it as an option. I understand their decision, but it's something that I really wanted (and I think some other Pushbullet fans would be interested too), so I made a Chrome extension that allows this behaviour.
This extension allows the Pushbullet browser extension to show phone notifications, even if the desktop app is also installed. To turn on/off notifications in the browser extension, set it in the extension's options, and to turn on/off notifications in the desktop app, use the desktop app's options. It's that simple. :)