Sometimes post spinal puncture headaches are caused by vasodilation of the blood vessels around the brain, which happens as a compensatory mechanism to restore intracranial pressure after the spinal fluid is removed.
Caffeine, being a vasoconstrictor may prevent this.
There are also some vasoconstrictive medications that also help prevent & treat these sorts of headaches.

Another type of headache that occur following the proceedure is due to intracranial pressure changes as one moves about.
Laying down also makes it easier for the body to maintain intracranial pressure after the proceedure; especially for those who tend toward orthostatic hypotension (low blood pressure when standing up suddenly).

Wtih love, Erika