Heck..we don't even want to get into a 'unions' and 'pension' and 'medical' discussion...that's for Friday!
You are right, it is an added cost. As a result, the company has to ship production overseas to another country where labor is cheaper. In theory, they will save in labor costs to make up for the tax increase. So I can see the point that the tax is forcing the company to go overseas.
However, the argument could then be that if the US labor force was cheaper, then the company wouldn't have to go to another country. You could make this argument about any "cost" a company has. Each country has advantages/disadvantages when it comes to its work force. In this case, production in the US isn't reasonable because higher labor costs along with a higher tax forces the company go to country with lower labor costs to offset the increased costs (overall costs). The company is taking advantage of trade because they have to pay the tax no matter where the cigars are made. Trade is the reason why the company is shutting down US production. So, if you like or are in favor of free trade, then you should be comfortable with this situation.