From what I read on their web page, the product is made for bare wood and you put it over varnish or some type of finish. OK, you followd the instructions, but used the wrong product.
The mineral spirits may pose a hazzard. It will give off vapors as it dries and the vapor can ignite. Not as bad as gasoline, but still a potential hazzard.
Renewing the top coat of varnish is easy. Staining the already varnished wood is a whole different story. That is what caused your problem from the start. Perhaps a different product would work. Perhaps a urethane with a tint will give you the finish and color you desire.
It will be if done right from the start. You will get many years of good use and little effort if done properly. Ed