Quick Facebook Chat is simply an app you added on your store for your customer to have an option to engage with you through Facebook. All notifications, messages will be on your Facebook page. So when customers will contact you through it, their messages will be directed to your Facebook page itself and you will reply to them through your Facebook page too.
To receive notification on mobile, you have to install Facebook Page Manager App. Please refer to the link below to download the app according to your phone's operating system.
To have a better management with your Facebook page, please refer to this link:
>> Connect with customers & convert them into sales via Facebook Messenger right on your store with Quick Facebook Chat. Get app for FREE.