Here's one way to do this:
Create a reference to your data in your Application. The Android Application is a good place to store global data. Next, populate the data via your AsyncTask (Watch out for the pitfalls of using an AsyncTask). You can now access your data via a call similar to this: ((MyApplication)getApplication).mydata
As you mentioned, two scenarios can come up. Either the data has been populated, or not. To handle this, use an observer that observes changes to the data. Have SecondActivity register as an observer when the data is null. When the data is available your SecondActivity's update method will get called and you can do whatever you please with it. Finally, make sure to unregister from being an observer. Hope this helps.