The keyword here is not "conceived." The most important words are "related to the business."
If your conception is related to your company's business, when you conceived your employment, it is the property of your company. Whether this kind of adhesion is enforceable in court is another matter. You signed the agreement to transfer your conception to the company and you must assign the patent, if filed, to the company.
Based on your situation, you had the idea during your employment. You reduced it in practice when employed. It does not matter whether you go to a competitor or incorporate your own corporation. I do not see otherwise.
