No, this is not correct. The correct way to say it is, "It's important to me that my employees be on time." The "to" in front of "be" should not be there. Alternatively you could say, "It's important to me *for* my employees to be on time," but that sounds a bit awkward and in that sentence you would normally omit the "to me."

It's almost correct - this is a great example of present subjunctive: "It's important to me that my employees be on time." So you need "be" instead of "to be". Present subjunctive in English tends to be formal, so you can write the contraction fully and remove "to me" if you want.

That's a great sentence! Yes, it's correct and I agree with you. When I ran a business, it was really important that staff turned up on time.