Not getting push notifications for mail

Hello,

I set up some email addresses in Mail (IMAP, for a business I started) this morning and I set up notifications so that I get banner notes and have "notification center", "badge app icon" and "show in lock screen" turned to ON for all the emails.

Everything seems to be working right except I don't get any notifications until I actually activate the "Mail" app.

I was hoping to get notifications when an email is received (the way my gmail app works).

Is there a setting I'm missing to have my emails pushed to the phone to trigger a notification instead of the app only checking for mail when I open it up?

I'm leaving it running in the background. I've tried restarting the app and restarting my phone.

Thank you