Who owns computer code derived from trade secrets?

We had a software engineer who joined our startup for two months. We only signed an NDA with him. The engineer was supposed to get equity but our negotiations broke down and we parted ways. During these two months the engineer worked on our existing code base and also added new functionality.

The engineer claims he is the rightful copyright holder to the work he created because he wrote new lines of code. However, all work made by the engineer was the result of us sharing our trade secrets with him. Certain functionality implemented by the engineer was also collaborated on between us and him and invented while he was involved.

Who owns the copyright for work derived from trade secrets? All code written is the direct result of us providing trade secrets to him. According to our NDA that both parties signed:

Title to the Confidential Information will remain solely in the
Disclosing Party. All use of Confidential Information by the Receiving
Party shall be for the benefit of the Disclosing Party and any
modifications and improvements thereof by the Receiving Party shall be
the sole property of the Disclosing Party.

I know we should have signed an IP transfer agreement as well but this was our first interaction with an outsider and the mistake was made.

Did you pay him (why founders should be paid )? If so, you can probably argue that the work was work for hire, and you own it.

If you didn't pay him anything, other than a promise to transfer shares (which he never received), then unfortunately he probably does own the copyright. You'll have to negotiate an appropriate settlement with him, paying him a cash settlement which reasonably reflects the hours and time he worked. Negotiate this in good faith and move on.

Note: I am not a lawyer, just an entrepreneur.