Let's look at the good points first -- no one was hurt. In your dream you successfully saved your cats and you were also unharmed. This is good!
Now let's look at the other symbolism, a "healthy full tree", "sunset", "house" and of course the main theme "fire".
I found it interesting that you noted that the tree was full and healthy. This struck as odd to you. I'm sure you also feel this same security in other things that appear healthy and strong, and don't fear them becoming hurt or lost to tragedy. But the reality is that regardless of how healthy and strong anything may seem, life itself is fragile, and accidents can occur, swiftly causing destruction. Again, your house, burned "like it was paper". This also shows the fear of delicacy despite appearance.
I'd like to bet you're not feeling very secure in your life right now. Things are changing and you are sensing that what felt sturdy and strong is no longer comforting. The realization that most things in life are "temporary" and not permanent is sinking in, and that's causing you to feel "unsettled". Maybe you lost someone in your life recently, or friend or relative had an accident or grew ill? Perhaps you are just going through a transition in your life. Or this could be a longstanding fear of insecurity.
But, despite all of that, you and your cats still stood! So, despite your lack of comfort, you know you'll make it. And you know what your priorities are. You could have considered your personal belongings, photos, etc. but you went in for just your cats.
Everything in life is temporary, especially our possessions, but even our feline friends and our own bodies. Nothing lasts forever besides bonds. Bonds are made with the heart and therefore run deep through our spirits. When we lose things in life, we don't lose them in memory and that's where they continue to live. That's why it is important to live in the present. Because if you always look to the future, you won't be making those memories for your future. These things shape us. Life runs in circles or cycles and even though it may not seem like it at the time, when you take a step back, you'll see that everything good comes back around in time, usually in a different form. Everything that you didn't really need goes away to let in new things. As we grow, we need more room. We need to discard our old skin so the new one can shine through.