The question asks, "Why am I in their life?" So, to me, this means what purpose does the querent serve in the man's life. So this is not a look at the querent's life, this is a look at how the man in question is affected by the querent's presence in his life.
I think I agree with your interpretation. The Emperor is usually the "my way or the highway" type of guy. He doesn't allow anyone to change his beliefs or values. He's very stuck and stubborn in his ways. But with the Tower here, this rattles his throne and knocks him off his feet.
I think the Tower here says that the querent may shake up how the Emperor once saw things -- the querent is shattering the foundations the Emperor once held. Maybe even a blow to the big ol ego he has.