You can achieve this by combining a few map event listeners and a variable as follows.
To prevent a tooltip when the user has moved or zoomed the map by mouse or keyboard you will need a variable that determines wheter your user clicked the "fly" button or not:
flying = true;
flying = false;
Then this code will execute once your map has stopped moving and zooming:
// tooltip or overlay here
See demo: http://jsfiddle.net/ft7s8son/