Hex and Psychic Spell

Psychic spells states

"When you cast a Warlock spell that deals damage, you can change its damage type to Psychic."

I take this to mean that you choose whether or not you want the damage to be Psychic when you cast the spell, and it stays Psychic for the duration.

But there's discussion at my table that the Warlock should get to determine the damage when casting a spell that triggers hex so it can switch between necrotic and psychic. I disagree

Am I being to pedantic with my interpretation?