How fast is it?

How fast does ACC react to the assistant action?

ACC itself has nothing to do with your assistant - we let IFTTT handle all that, so the speed of the reaction depends solely on the cloud application that is used (Dropbox by default).
It helps to have a good internet connection, but the rest is just how fast Dropbox syncs the file to your computer.

So, Answer: as fast as your cloud service syncs files.
From experience, it's usually about 5 seconds for a moderate internet connection, down to 1-2 on higher-end networks and PC's.

Advanced section;
If you're using ACC for something else than assistants like Alexa, the reaction time is down to 0.01ms (so, instant), from the moment the action-file is created in the listener-folder.