It overlapped... I started expressing my interest in design while I was completing my degree, in the form of small projects and getting a few clients on board. This was mostly things like posters for local bands, or a menu for a small restaurant in town. At this point I was just interested in growing my portfolio and getting some experience under my belt. I would take any job I could get, even if I didn't know what I was doing! I'd have prospective clients tell me they want a new website with a CMS and integrated commerce, etc. and I would nod my head, go to a local bookstore and read the books I need to in the store (they were expensive, so I couldn't buy all of them!)
This allowed me to essentially bankroll my education in design and programming, as each client was a learning experience. Probably risky, but for the most part it worked out.
I think the one huge thing I picked up in university was the ability to learn quickly: I was taking 6 courses at a time, and if you missed a lecture or didn't understand something, you'd fall behind pretty quickly. It forced me to develop the ability to read, absorb and understand new material very quickly, which no doubt has helped me learn what I needed to as I began my career in product design.