Replacement effects are unaffected by Wizard's Staff's second ability.

The second ability doesn't copy the triggered ability; it just causes the ability to trigger an additional time. Any choices made as you put the ability onto the stack, such as modes and targets, are made separately for each instance of the ability. Any choices made on resolution, such as whether to put counters on a permanent, are also made individually.

In some cases involving linked abilities, an ability requires information about "the exiled card." When this happens, the ability gets multiple answers. If these answers are being used to determine the value of a variable, the sum is used.

Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]." Some keyword abilities are triggered abilities and will have "when," "whenever," or "at the beginning of" in their reminder text.

If a triggered ability is linked to a second ability, additional instances of that triggered ability are also linked to that second ability. If the second ability refers to "the exiled card," it refers to all cards exiled by instances of the triggered ability.