We don't know the employer's IP clause. I've certainly worked for companies which claim ownership of only IP directly discovered in the course of doing the company's work, related to the company's work, or using the company's equipment.

With that being said, OP is probably doing the work from his employer's office, which is definitely a breach of any employment contract I've ever signed.

However, that still isn't illegal. That would be a civil dispute. "Illegal" is implying that he could go to jail and that he is breaking a law. Just nitpicking, but I think that "illegal" is a much stronger idea than simply "could get you fired or could get you sued."

I think it would still be a civil matter, just as patent infringement is.

It would more likely be a breach contract.