This is so so sooooo normal and as far as I know, no it does not go away. My moms youngest is 18 years old and she still gets them.
My doctors theory (theres no 100% known cause) is that muscle damage sustained in pregnancy (no matter how healthy you are, stretching that far can cause some amount of artificial damage... which is the sort that would cause this) is trying to heal itself. To do so, it is twitching. This explains why I feel it all over in the tummy but most often in the area where my babies kicked/stretched the most. Also explains why I have SEEN it (rarely, but I have!)
Right now they will seem more prominent/obvious because you JUST had that baby, just a couple months ago you were still feeling that feeling with him in you.
As time goes on I do not know if they get less frequent or we just get more used to them but most women I talk to about it seem to feel it less.
Artist, photographer, stay-at-home-mom and Marine wife. Mom to 4; a boy and three little girls.