Restoring from Time Machine to different type of Mac
Actually that is, in most cases just fine.

I've been restoring my user profile on an older Mac to a newer Mac since the Migration Assistant was available on OSX. And I always do what you just did, restore everything.

That said, if you were having issues with your networking on the old Mac then it might carry over to the new Mac. But I have never seen restoring the network settings to a new Mac cause the new Mac to misbehave in any way.

That said, just because I didn't have any problems doesn't mean it can't happen. You could go through your ~/library/Preferences and /Library/Preferences folders, delete any networking related files and reboot. That would likely tell you if that was the problem.