Are there any health concerns with using copper green wood preservative indoors?
Your contractor should not have sprayed that stuff inside your wall for a number of reasons:

1) it says on the label that it is for exterior use only.

2) It will not really do any good. That product is similar to many traditional wood preservatives that utilize copper napthenate to treat wood before it is exposed to moisture. Putting it on after the fact is arguably useless. It is commonly used for wood that will be left outside without a protective finish. Pressure-treated lumber is treated with copper napthenate, that's why it is green.

3) The stuff is smelly, and covering it up before it was dry (if that's what he did) will prolong the drying time. 

The product "carrier" is mineral spirits (paint thinner); oil-based paints using paint thinner or turpentine as a carrier solvent have been used indoors for a long time. The "danger" to you is likely minimal. The TLV (Threshold Limit Value; which is how much an average worker can be exposed during an 8-hour work day with no respiratory protection and no significant health effect) is 500 PPM (parts per million) for Green Products Co. Copper Green. Without a detection device to measure you can't really assess your exposure level, but opening a window nearby to provide ventilation will significantly reduce the concentration.

You will have to make a "trouble vs. gain" decision on whether to have it ripped out. Opening the wall and providing ventilation to ensure it dries would fix the issue. Once dry, there would be no real reason to further "seal" over it unless irritating odors persist.  

Material Safety Data Sheet