It's true that, when you take an action in Asana that causes Flowsana to make other change(s) to your Asana information, you won't see the Flowsana change(s) instantaneously. In general, you should see changes occur within 5 to 15 seconds, but it can sometimes take longer.
Why? The simplest answer is that there will always be some latency involved; you'll never see instant changes. There are a few reasons for that. First, it just takes a bit of time for Asana to communicate to Flowsana that a task change has occurred, then for Flowsana to figure out what to do, then do it, then communicate the change(s) back to Asana, then for Asana to make them. Second, Asana is slower in writing than in reading, so it takes Asana a little time to record the change(s) (if you're interested in the technical nitty-gritty about this factor, you can read more about it here: https://forum.asana.com/t/api-requests-are-slow/102985/8).