- Correction: Yahoo does not support IMAP IDLE (the industry standard for push mail), so it's scheduled mail sync only.
- And one more thing:
You'll want to use Yahoo's web mail to check how it's working in Aqua.
Mail apps don't sync with each other -- mail apps sync with mail servers.
If Aqua <-> Yahoo web mail is working correctly, but Yahoo web mail <-> desktop mail app is not, then you will need to do something in the desktop mail app, not Aqua.