Why do you use both the app and email? If the reason is that you want notifications as soon as possible, I think that you could use what's called "direct data text"... where the camera emails a text message to your cell phone. Here's the "direct data text" email addresses for several carriers:
Have your camera email to your cell phone 10 digit phone number (in place of xxxxxxxxxx):firstname.lastname@example.org
(if your cell phone is ATT)email@example.com
(if your cell phone is Verizon)firstname.lastname@example.org
(if your cell phone is T mobile)
If you want to continue using email, as you have been, here's an idea:
As Johnny mentioned, email providers often tend to lag on sending messages; some are worse than others. Try a free Outlook.com email account...I bet it will be more reliable for you. iPhones don't instantly push (receive) emails, even if the settings are set for push). Using an EAS (Enabled Active Sync) email account will allow an iPhone to instantly receive an email. I use a free Outlook.com email account on my iPhone, as the Outlook.com accounts are EAS.