I can confirm the issue, running OSX 10.9.1.
exchange 2013 CU3 (latest release) in combination with mail app 7.1. (1827)
push does not work. fetch setting on 1 minute does work.
iphone/ipad push works great, new email on server, directly delivered on mobile.
I think because the implementation of mail app and iphone/ipad is different, the activesync device registers itself on the exchange server (for remote wipe of the account), there for the exchange server is allways aware of the mobile device.
iphone/ipad uses /activesync directory with a listner service.
The mail app, uses /EWS (exchange Web Services) what means it communicates stand alone to the exchange server. (like a pull mechanism. with a polling interval.
Outlook 2011 also uses ews, and the push functionality does not work also like your mobile communication. (delay is about 20 tot 30 sec.)
Outlook for windows uses a different technique (MAPI) and communicate with RPC over HTTPS and push is immediately. (uses a listner)
so, i think that or the EWS needs to be changed on the exchange server side to accomodate same principal as activesync (apple/android/windows phone devices)
or
mail app/outlook 2011 need to have a shorter pull interval automaticly configured....
i think microsoft and apple needs to work on this case to figure out the best way....
put your mac mail app client on 1 minute pull, that is the shortest work around.
regards,
Leon