If a Triggered Ability says “you may”or “they may” as the first part of its Effect, the controller of its source will choose whether or not to perform the Triggered Ability during finalization. Example: Tideturner reads “When you play me, you may choose a unit you control at another location. Move me to its location and it to my original location.” This “you may” appears as the first part of its effect, so the choice represents whether or not to perform the triggered ability. 1. The decision of “may” when it appears in this way is solely whether or not to perform said triggered ability. 2. If the controller of the Triggered Ability chooses not to perform that Triggered Ability during finalization, it is removed from the chain and considered to have not triggered. 3. If “you may” or “they may” appears in any later part of the Effect of a triggered ability, it is decided on resolution. Example: Ornn, Blacksmith reads “When you play me or when I hold, look at the top 4 cards of your Main Deck. You may reveal a gear from among them and draw it. Then recycle the rest.” This “you may” does not appear as the first part of its effect, so the choice is made on resolution. The ability is always finalized to the chain.
§ 383.3.a Core Rules PDF (officieel)
§ 383 Triggered Abilities are repeatable effects that happen when a Condition is met.
§ 383.3 When a Condition is met, a Triggered Ability behaves like an Activated Ability and is placed on the Chain.