Anointed Procession says
“If an effect would create one or more tokens under your control, it creates twice that many of those tokens instead.”
Kalitas, Traitor of Ghet says
“If a nontoken creature an opponent controls would die, instead exile that card and create a 2/2 black Zombie creature token.”
Rule 609.1 says
“An effect is something that happens in the game as a result of a spell or ability. When a spell,
activated ability, or triggered ability resolves, it may create one or more one-shot or continuous
effects. Static abilities may create one or more continuous effects. Text itself is never an effect.”
Kalitas' ability is the effect creating the tokens. Kalitas only cares about when a non-token creature dies, not how.
If a player controls Anointed Procession and Kalitas, and shocks a non-token creature that then dies after, they should still receive two 2/2 zombie tokens.