FaceTime Missed Call Badge Remains After Recents Checked on iPhone

I have FaceTime set up on my iMac (Mavericks 10.9.4) and iPhone 5 (iOS 7.1.2). When I miss a FaceTime call, the missed call badge appears on both FaceTime icons (iMac app and iPhone app) as it's supposed to. When I open the iPhone app to check my recent/missed calls, the missed call badge goes away. However, it remains on the iMac FaceTime app icon until I also open that app to clear the icon. Aren't the badges (like everything else) supposed to sync? If so, does anyone know what may be causing the FaceTime app on my iMac to fail to recognize when I've already reviewed missed calls on my iPhone and accordingly remove the missed call badge?

Thank you in advance.