Vader is looking for Luke cuz he knows that Luke is his son and has plans to overthrow the Emperor....all unbeknownst to the Emperor.
Between Luke destroying the Death Star and beginning his training with Yoda...this would be the disturbance in the force that the Emperor mentions.
The Emperor feels this disturbance and then somehow found out the name of Luke skywalker (how he found out - through the force or some other means - is not mentioned), thus contacting Vader to tell him about it.
So the Emperor didn't know shit and Vader knew everything and had his plot down. vader could have covered up the whole search for skywalker by just saying that he's looking for the rebels rather vehemently.
It requires the viewer to fill in some blanks...but it's reasonable and logical all the way through.
Now...here's one for you that is Lucas really fucked up on.
In episode 3, Vader asked sidious what happened to Padme and sidious said that vader killed her. Now in ESB, Vader has a son. Doesn't he suspect that sidious is fucking lying to him?!!?!?!? That something it NOT RIGHT!!!
Interesting food for thought there....