There is a good talk by one of the engineers who worked on the initial prototypes, and IIRC they both require and are able to achieve something like nm accuracy when they sweep the rotating masses with the lasers on them (That is, not only is the frequency very precisely controlled, the phase cannot drift either). With the help of some custom components they can do that for a hundred bucks.
I'm slightly hesitant to go into it for mostly ethical reasons, but military technology has always fascinated me if purely because of the toys they get to play with. The amount of gear even a World War 2 aircraft had by the end of still surprises me, i.e. The Mosquito had a primitive version of what we would now call a HUD displaying a radar horizon and a gunsight. Know-how and an unlimited budget go a very long way.
By the time the laser reaches the target receiver it could be covering an area of tens of meters, or grater, and still be usefully detected.
Think about the tiny amount of energy emitted by a mobile phone transmitter and still able to he usefully detected by an antenna on a tower kilometres away.
Either way I have no idea how they work out the firing solution for the comm lasers with sufficient accuracy. Hypothesizing: maybe they shoot multiple lasers, the main comm laser and a alignment pattern with auxiliary lasers which could be used for targeting feedback?