It could have been Safer's De-Moss Cryptocidal Soap, a commercially available environmentally friendly soap solution. (Active ingredient is POTASSIUM SALTS OF FATTY ACIDS)
A certified Arborist would likely have sprayed your neighbor's trees, but a license for it's use, is not usually necessary. (Check with local officials, if unsure)

If moss is a pervasive problem in your area, you can probably find the herbicide at local nurseries, big box stores and home improvement centers. Usually sold in one quart containers. One is a concentrate and has a hose-end connection, one is a diluted formula and has a trigger sprayer.

When using it, follow label directions and as a precaution, wear protective clothing and tightly fitting goggles. It can cause eye and skin irritation upon contact.
Good luck!