Default AT&T LG G2 and Exchange Email Problem / Question

I am a long-time Exchange email user, and just recently purchased the LG G2. I do not like to have Exchange Mail push turned on, as it unecessarily drains battery. So, on very device I've had in the past, I've set push to "never" or "manual", or whatever the choice may be. On the G2, you have peak time setting and off-peak time setting. I've set them both to manual. To me, that means that the app should only search for / download new mail when the app is open. This is not how it is working. The phone is receiving new emails constantly, automatically, even when the app is closed (totally closed, as in nothing open in the recent apps tray). How can I stop this from happening and set it up the way I want it to behave?

Thanks!