According to wikipedia the 1859 Carrington Event was caused by a coronal mass ejection (CME) of plasma.
As it's plasma and not photons it stands to reason that the CME would not be traveling at the speed of light but how fast would it be traveling at? Or does that amount vary?
Of course just because the CME is traveling at a certain speed it doesn't necessarily follow that we'd instantly detect it the moment it left the suns surface either.