Here in the UK, this is normally covered in the contract via 2 different angles. To summarize very briefly:
(a) You have to notify the employer if you have alternative employment
(b) Any designs/inventions developed whilst with the company must be handed over
It sounds like you fall more into case (a).
My take on this is that the company wish to be kept in the loop if there are any hours you would not be able to work. Additionally (although unlikely), it could be possible that the 2 jobs might conflict e.g. both companies may ask you to work on a given weekend.
It is also perfectly reasonable for the company to know what other work commitments you have. If they know you have a second job, they may wish to allocate some of your workload (which would otherwise be done in overtime) to another employee.
The arrangement could well be a temporary one. A colleague of mine took on a number of part-time jobs while his wife was on maternity leave. He notified the company and assured them it was only a temporary measure and they did their best to ensure that meetings/client trips weren't scheduled when he had other work commitments.
Seeing as you're not in effect employed by a second company, it is moot as to whether any of this applies. You're really just developing an idea which may or may not turn out to be an alternative employment opportunity.
If however you're developing an idea which might cause you to ultimately become a competitor, then this is different again - case (b) territory. You might think you have to burn your boats once you start your new venture but this is not always the case. Depending on the culture of the company, you could become an intrapreneur. You get to work on your idea while the parent company shares the risk, provides the premises and the materials and you are largely just left to get on with things. They will of course take a substantial cut of the profits themselves for providing all this, but it is an alternative you may wish to consider.