Yes, Hotmail is in the process of upgrading the back-end to support IMAP IDLE (push mail) and a bunch of other things. Not all accounts have been upgraded yet.
But are you really saying something else - that the app isn't checking mail in these accounts at all? It should be, every 15 minutes with the default settings?
Most common reason: various "memory optimizers" and "battery optimizers", either third party apps or things built into the phone / tablet:
- Clean Master - third party app
- MIUI - system setting, covered in the FAQ
- Huawei - system setting:
http://www.aqua-mail.com/forum/index.php?topic=3181.msg15336#msg15336"It was the program to save energy from Huawei"
- Sony - built-in "Stamina Mode"
In general Android 6+ and so called "Doze Mode" which restricts apps in the background after a few hours:
- AquaMail settings -> mail, receiving -> will have a panel / prompt to whitelist the app for this "Doze Mode" if it's not already