The way I read it, private companies would not be affected. The law is for municipal police, fire and ems only.
FWIW, this country needs less union involvement, not more. Unions when they were created served a purpose. They fought for employee safety, and fair working conditions, overtime pay, etc.. They are no longer needed today. We now have OSHA, and labor laws to protect employees. Today unions are all about greed and money. The union entitlement mentality is what has destroyed this country. Auto workers making $75.00 an hour to watch a robot assemble a vehicle, construction workers making prevailing wage to do the same job that others do for half the price (my full time job is a non-union electrician), and now there is another thread going on this site where a new EMT thinks that a union should be able to get them $25 an hour for their advanced medical knowledge (110 hours of first aid training). There are thousands of people willing to do this job for free, you're lucky to even have a job making $10 an hour!
In my area teachers unions, fire and police have all made big issues about wage increases, health insurance contributions, and other contract issues. It seems that they feel they are immune to the economy. Meanwhile, average citizens have gone without raises (I haven't received a raise in over 2 years), have dealt with insurance premium increases, furlows, and other benefit concessions.
Unions are out of touch with reality. They want more, more, more. Unfortunately they don't realise there isn't any more money available to give. Wages are (or should be) set by the free market. People are only worth what the market says, supply and demand. Union strong arm tactics cannot change this basic principle, although they try.
Less entitlement. More hard work, earn your paycheck, live in reality, and this country would be better off.
/rant