Here's an idea. Load your data ahead of time and store it in the UserData property of your button. That can be done anywhere in your code.
app.Button.UserData = data;
Then when the button is pressed and the ButtonPushedFcn callback is executed, you can move the data from the UserData property to the UItable.
function ButtonPushed(app, event)
app.UITable.Data = app.Button.UserData;