Cap said:

I think it’s clear enough that they both know they’re on the same page, but if you don’t agree, then wouldn’t it make sense for the Emperor to “test” Vader? Vader has just said “I have felt it” and “Yes, my master.” Think of the Emperor’s omission of Skywalker’s identity as saying, “Are you just pretending to know what I’m talking about, or do you really? Prove that you do by telling me.” Vader passes the test by saying, “He’s just a boy. Obi-Wan can no longer help him.”

I can't believe that there is still a misunderstanding of this scene!!

The whole galaxy by this stage knows the name Luke Skywalker, the hero of the rebellion. Vader knows Luke is his son, as the kid was involved with Kenobi's disturbance on the Death Star, who was travelling on a ship which escaped from Tattooine. Vader had sensed that this boy was strong with the force, but in the period after the destruction of the Death Star, Luke could not improve his abilities until he met Yoda. This meeting sent tremors in the force, something was happening in the galaxy which could upset the position of Vader and Palps.

'There is a disturbance in the force', someone is being trained (or will be, remember Palps is forseeing this, like Luke feeling the pain of his colleagues on Bespin)

Vader has felt this also, 'Obi Wan can no longer help him' & 'The son of Skywalker must not become a Jedi' again supporting the fact that they sense that Skywalker is being educated.

They both already are wanting Skywalker for their own means as master and apprentice & father and son.

Palpatine at this stage has forseen that Young Skywalker could mean the end of the Sith, which Vader mentions to Luke at the end of Empire & in Jedi