Please check how exactly you'd set up the account in Aqua Mail:
- Long press on the account on the app's main screen
- Options and folders
- You'll see one of: "Exchange options", "IMAP options", "POP3 options", that's how you'll know.
Exchange, IMAP, or POP3 are different ways to connect to a mail server.
Out of these, POP3 does not provide any sort of read/unread back and forth sync with the mail server (so a mail app uses its own logic and storage to track read/unread messages).
If it is indeed POP3, please remove the account from Aqua Mail (long press on it, choose Remove account) and add back, making sure to use either Exchange mail (in the account type popup) or Internet Mail (same).
For the latter, since Internet Mail can be either POP3 or IMAP, please tap Manual after entering your email and password, and be sure to select IMAP (top of the screen) and to enter the right server settings (server name, encryption, port #) for IMAP.