Hmmmmm...... you get a message that says you can't run AE on your current OS.... yet you don't mention the version of your current OS.
See the problem?
Dave, his OS is mentioned in the thread title. Max OSX 10.9.3
Oops. Thanks for catching that, Szalam. Apologies to the OP: I didn't read that for total comprehension.
Apologies Mr LaRonde, i'll be sure to include full details in both heading and body in future.
Anyway, i fixed the problem.
So initially CC was telling me all my adobe CS6 apps were up to date, green ticks across the board. Then I uninstalled and re-installed After Effects, and this seemed to kick CC into gear as it then announced available updates for all my CS6 Production Premium applications. I updated everything, including After Effects and BOOM. We're in business.
TL/DR: CC wasn't spotting any CS6 updates for some reason. A reinstall sorted it.