Maybe some legal experts need to chime in here, but where are the laws saying I need to do what police say, even on my own property, and if I don't I can be justifiably shot?
Not to my knowledge. Police don't have any more of a right to shoot someone than you do. They do have a more explicit mandate to use force when necessary to accomplish their tasks (fighting crime and providing general security), but that is limited to what's reasonable and non-excessive. They can only shoot someone when necessary to protect themselves or others from a reasonable threat and when no other means were adequate in the situation. There's a lot more (and arguably too much) leniency when judging this than there is with your average citizen because being a police officer is already a dangerous job to begin with, but you cannot be justifiably shot for not complying without there being a real danger to the officer or others.
It's why these mishaps should be looked at on a case by case basis. On the one hand, the guy ultimately didn't have a gun, committed no crime and probably only dropped his hands by accident, because he couldn't hear what was said or because he was just overwhelmed with what was going on. In retrospect, there was no reason to shoot. On the other hand, the police was called there to respond to the shooting of a man and a hostage scenario where others were likely to be killed and the entire house set on fire. The US is a country with very high rates of gun violence and firearm ownership, so its officers are trained accordingly to expect or be prepared for a potential gun in every situation. When you're under the impression you're dealing with a murdering lunatic in the process of murdering his entire family, a man suddenly lowering his arms to his waist can easily come across as someone reaching for a weapon.
The police were clearly in the wrong, but it's not always that easy to judge. This is for a very large part caused by the American gun culture that necessitates law enforcement to be trained in an almost combative way because every situation can potentially and very easily turn deadly due to the likelihood of a gun being involved. Almost 150 police officers were killed in the US in 2016. That's nearly 3 per week. Thousands more were assaulted with firearms the same year. And that makes it a lot more understandable why a nervous cop is a bit too quick to pull the trigger.