Feline Saboteur timing

How does it work at ANI OBF? Do they replace the card they discard and then get milled, or do they replace after the milling? Thank you.

Name: Feline Saboteur
Cardtype: Action
[ani][obf] Choose any Methuselah. The chosen Methuselah discards 1 card at random from his or her hand.
[ANI][OBF] As [ani][obf] above, and the chosen Methuselah burns the top 4 cards of his or her library as well.
Artist: Kieran Yanner