Nope, it's not done right.
For example, suppose you have an iPad and an iPhone. Somebody sends you a message -- and it goes to your iPad, but not your iPhone. But your iPad is at home, so you don't get it for hours. Or maybe your iPad has been dead for a week, but it was still logged into iMessage when it died, so it's still getting the messages rather than your phone.
Yes, there are ways to make it work, but you've got to be aware of the problem and stay on top of it, being careful of what you let into iMessage. (And yes, that iPad will keep trying to do it!)
And it's worse if you have an iPad and an Android phone, because the Android can't log into iMessage at all, so anybody who sends you a message via iMessage will have it go to your iPad.
If you want people to reliably get your messages and to reliably get theirs
Facebook Messenger is more of an example of it done right -- messages go to every device.