In the following paper from I. Bernard Cohen, "Roemer and the First Determination of the Velocity of Light (1676)" published on Isis (1940):
Can be read:
explaining that the delay would arise from the simple fact that astronomers considered light to be propagated instantaneously rather than gradually
I'm not sure I understand what this means, Roemer is defending that light is not instantaneous. Isn't the delay meant to prove that the light propagates gradually?