For some reason (mainly because it's poorly coded) Publisher uses an image map to use your links, the problem with this probably being that it's unsupported currently. If you want to fix this you're going to have to migrate to something different. Because doing it in publisher isn't going to happen. I suggest learning to code HTML:
http://www.w3schools.com but apart from that fixing this problem is literally a re-write of your code.
Cheers,
Jamey