Yes, you are supposed to find multiple Pokemon. It's different to PokeRadar chaining.
Also, it's normal for the chain to break. What you need is to lead your party with a Pokemon with the ability Suction Cups. It will guarantee that a Pokemon turns up on your rod, 100% of the time. This is the best way to do chaining, and is pretty much responsible for the swarm of Shiny ocean Pokemon in trades.