You can avoid making your explosions into squares if you animate them in a space that is much bigger. As well as not animating all the way to the end of that space. What this shows is all the particles from the smoke just end at around the same time and place. And the reason for this I suspect is instead of animating each particle 1 by 1 you animated them all at the same time for each frame.
It's much easier to animate particles when you focus on 1 at a time. What I mean is you work on one particle all the way to the end of the animation then go back to frame 1 and repeat till you are satisfied. It allows you to vary the speed, the trajectory, and overall destination. This will also help with each piece fading out on it's own time as opposed to fading out at the same time as all the others.
However it is very smoothly animated. And the colors work really well too.
Nice done! It is a pity that the smoke disperses in the form of a square!
..tell me plz..
this is really great. nice detail and colors