When is it best to break Hearts?
There's a couple of things that are important when deciding what to play when you can't follow a suit:


Is it at all likely you can take all the points with this hand? Then don't throw any points at your opponents.
Are there any cards you need to get rid of to avoid catching points yourself? Examples are the Ace or King of Spades, or a high Diamond. When you have a lot of Diamonds, chances are others can't follow Diamonds and throw in points themselves when you are forced to play the Ace. This can become very costly if all you have is more Diamonds to play. If you still had that little Heart that you threw out instead of Ace of Diamonds, you could have played that and forced another player to take it. 
Is it possible that the opponent taking the first point, takes all the points? Sometimes you'll regret tossing away that one point when you get 26 added to your score at the end of the hand.
Does the ability to lead Hearts give an escape to a player? If a player is forced to lead Spades (and cut in on his own AK in Spades) because he isn't allowed to play Hearts yet, that might be an advantage also.


Conclusion: Don't automatically break Hearts when you can't follow suit. Think of the long-term game, there's plenty of tricks still coming.