Honestly? I don't know if I'd care much. If it turned out to be a perfect clone, I'd probably be a bit irritated, but in the end, imitation is the sincerest form of flattery.
I've been involved in a few tiny ventures (only me, or at most one other person) and one thing they've all had in common is that none of them were unique except in the personal approach I took to them.
So, as an example, you could start a business producing readers for diesel fuel flowmeters as I did, but would you have the same approach to customer service as me? Would you go out of your way to make using the unit as easy for your customer to use as you could?
The employee scheduler is the first software-only project I've ever done (and it was started primarily to learn web development), so maybe my reaction to being cloned would be different. But in the past I've built and sold hardware devices that had plenty of cheap marketplace competition so I'm used to that. My approach was to not care how many people were building the same thing or how much less they charged, but to focus instead on how happy I could make my customers.
I think of the product as a means to an end. The desired end result is profit and happy customers. The product or service is just the route you take to get there and really not that important in itself.