Is the droplet running an applescript? If so, it's better to have Hazel trigger it. It appears the droplet is not locking the file so Hazel can't know that it's finished. If you do it all within Hazel, then, except for certain actions like the "Open file" action, it can do things in proper sequence.
Otherwise, is there some way to differentiate between the file before and after the droplet has processed it? If so, try and work that into the rule conditions. Or add logic to the droplet to add something to distinguish it. Like have it set the color label when it's done.
Alternatively, you can put in a pause (via a script) though I don't know how consistently that would work depending on whatever it is that this droplet does.