Not precisely, if I understand it correctly (and I might not). It would appear to to someone observing the point of origin through light-waves, but to take my earlier example, while you might be observing the earth as it was 10 years ago from a point 10 light-years away, the earth isn't actually 10 years younger--that's just how long the light took to reach there. If you sent an ansible signal to earth, you wouldn't see an instant result--you'd have to wait ten years for the light waves carrying the result to reach you.
If I'm wrong, please someone explain how and why.
I see what you're saying, and it seems correct intuitively, but a lot has been written on the causality problems of instantaneous communication across large distances, so I would reckon there must be something to it.