As the owner of mastiffs for a few decades I'll say that is not typical of the breed. Regardless, you IMO, had the right to do whatever was needed, including shooting the mastiff.
Owners that can't control the dogs shouldn't take them out in public. Hell, they shouldn't have them.
I go out of my way to be a good neighbor with my dog. Many dogs react to the size of the dog so when an unknown dog walks by I'll insure my dog doesn't take up any aggressive body language/postures, doesn't stare, or any of the other behaviors that cause dogs to react with aggression, or panic and start to drag their owners around, barking, squealing, trying to fight etc.
Often owners will want to stop and see the "big dog", and ask questions about it, but their dogs don't. Unless the owner is in control of their dog, and both seem calm I avoid both.
Your reaction to protect your family is strong enough to make you jump on a dog that could remove your arm from your body as easily as you could bite a potato chip in half. That says a lot about the love owners have for their dogs.
I'd reccomend notifying the authorities as if the dog in question did it once, it will likely do it again to someone else.
Also, there are different breeds of mastiffs, some bigger, smaler, more aggressive, less aggressive etc.
The kind I have is the "english mastiff". The largest, and probably gentlest of the mastiff breeds.
At 35 inches at the haunches, a 36 inch around neck, and 220lbs he ( Finn, in my avatar) is nowhere near the largest male english mastiff I've seen ( or owned in fact). None of them have ever shown any inclination to be dog or human aggressive.
Bullmastiffs, Neopolitan mastiffs, French, himilayan, St. Bernard, etc. all as different temperment as to be almost a different breed.
A true English mastiff is fairly rare. Mine came from a breeder in the next state over, and a pup cost $1500, which is about average depending on bloodline & sire.
Last I checked the English mastiff had no occurences in the insurance registry iof dog attacks & deaths in this country. Joe