I think you are mistaking an nda with a non-compete agreement.
An nda simply prohibits you from disclosing your activities and other information the company deems private. A non-compete is what would prohibit you from operating a business in a manner that would compete with your employers business.
Bottom line neither sounds to be an issue here.
What you may may be thinking of is an employers rights to patents and ideas created during your period of employment. Aka work product or work inspired product.
An employer does not need to have you sign anything relinquishing rights to work inspired products although many do. An employer has a right to work inspired product simply because it is work inspired product.

