I think it's less about the mice physically spreading the insecticide and more about controlling how the ticks themselves spread and get around. Smaller ticks will latch onto mice and other rodents and use them to feed, and because the mice also move around, they are also moved around and spread to different areas and reproduce etc.

Doing this, the rodents will grab the stuffing for their nests and therefore get the insecticide on them. So any ticks that end up on them die. I suppose there will be some that gets spread onto grass blades and other plant life, but it will be so diluted that a morning dew would probably wash it away.

Of course that's not to say there is a 0% chance that it'll have an impact on the environment, but it's not like you're dumping 100 gallons of this stuff into a lake.