Hi, i think is good idea implement a keyboard shorcut for manual synchronization,
I have found that while the open web application on one screen, such that the tasks Today..para sent by email appear in the inbox, I have to force synchronization
Meanwhile, in Windows you can press F5 to refresh or press the browser's refresh icon. Hope that helps for now.
In the longer term, I think Doit should sync automatically, continually, like so many other apps.