You've done nothing wrong, systems have to be manually moved around on that map. Shift click to drag them around, and click on the sys pos button and then save positions to keep them where you want them.
So this is my first game, and I have found a couple of other stars, but when I go to the galaxy map thing, it looks like this: hxxp: gyazo. com/9eb904e4c8a0f33e50117aa1ca0ae4c3 <--- Link to picture.
I dont know if I have done something wrong, or if it is some stupid bug, but please help me!