I just downloaded this app on my iPhone (iOS 7.0.2) and am trying it out. I also have a chrome plugin.
I created a task in inbox on my phone and set the due date as today 3:00pm. 3:00pm passed by and i didnt see any notification on my phone or in chrome.
I tried creating a task from the chrome plugin with a 3:05pm due date for today. still no notification.
the badge app shows the no. of tasks due but i dont see any notification. Is it a bug or a limitation of the non-premium account? I would like to assume, that notifications are a standard feature and reminders is a premium feature.