I know that's a weird explanation, so consider:
t0: S~~~>O U (shadow exists)
t1: S~~~~~~> U (shadow exists)
t2: S~~~~~~~~~>U (shadow !exist)
At time "t0", "U" thinks he's in the shadow.
At time "t1", "U" thinks he's in the shadow.
At time "t0", "U" thinks he isn't in the shadow, since the photons are now hitting him.
A similar calculation/thought-experiment can be done for shadows with "angular momentum", in case you think the tangential velocity of the shadow will exceed the speed of light.
t0: SO U1 (U1 in shadow)
t1: S~~~~~~~~~~>U1 (shadow leaves top first)
I didn't do the precise math, but I'm pretty sure the tangential velocity of the shadow along the dotted line won't be greater than the speed of light. The curvature of the "wave front" formed by the tips of the arrows ">" above will be lesser than the dotted line curvature, so the photons near the top of the diagram hit the dotted edge before the ones towards the bottom. This is because the source, S, takes time to move away from O.
Note that the wavefront formed by the photons moves radially outward from S, but ascii art is limiting.
There are similar things that appear to exceed the speed of light:
See "group" and "phase" velocities for similar things to the lighthouse.