Why does Event Horizon affect Vladimir while in Sanguine Pool?

All spells that get cast before he enters the pool stay on Vlad (ignite, fiddle drain etc.), and Veigar's cage is considered one of these spells. It also affects flash and all other dashes. So does Jarvan's Ult.

To add to the answers/comments, Sanguine Pool also prevents certain things by allies from affecting Vlad. Some examples include Sona's heal Soraka's ultimate, and Will of the Ancient's aura effects. Check out the notes under Sanguine Pool

It affects him the exact same way any other non-targetable Crowd-Control effects would affect him, aside from Knockups and Displacements, like Malphites' Ult, Alistars' Q and W, Blitz's and Nauts' Pulls, etc.

Stuns and slows still affect him while he is in his pool, as stated in the ability description Mindquake provided. Similarly, On-Hit spells that apply a CC effect (Morganas' Dark Binding, Frozen Mallet, Phage, and Rylai's Procs, etc) will fail to apply them as he is untargetable. However, if a Proc or an on-hit effect lands before he goes into his Sanguine Pool, he will be affected by them still.