Why do I have to fetch mail for each account separately?

I think this is only happening on my IOS devices (iPhone and iPad Pro) but I'm gonna monitor my iMac as well. So on my iPhone which gets the most use and charges every night... it seems that when I look at the "All InBoxes" tab, my newest emails are not there. When I slide down to an individual email account, it updates on the fly and then those new emails show up the All Inboxes listing. So then I have to go to each of my email accounts separately and they then update as well. Isn't there a way in settings to download new, incoming emails instantly as they come in and show them in the All Inboxes list? This is a real nuisance for me with multiple email addresses.-Mike