Earlier quoted context omitted.
He built it during University, so before he started working for the employer. They may have a legitimate business concern, but that doesn't change the fact that it's Nick's IP and he can do what he wants with it.
Undergrad or post-doc? If post-doc, humorously, in this day and age, this would likely mean the university owns it, rather than the employer. Undergrad, a number of universities have started having students sign agreements giving them rights, but most don't.
Most universities, or most students?