If these are not iCloud accounts and are IMAP accounts, then maybe they're simply being marked read on the laptop before the phone checks for new mails.
MacOS uses IDLE which is a kind of pish mechanism for IMAP mails. iOS doesn't support it, so will fetch according to the schedule (min ever 15 mins) you've set in settings.
MacOS uses IDLE which is a kind of pish mechanism for IMAP mails. iOS doesn't support it, so will fetch according to the schedule (min ever 15 mins) you've set in settings.