Twinflame Travelers's 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. For example, if Elite Arcanist's enters-the-battlefield ability triggers twice, two cards are exiled. The value of X in the activation cost of Elite Arcanist's other ability is the sum of the two cards' mana values. As the ability resolves, you create copies of both cards and can cast none, one, or both of the copies in any order.

Abilities that apply "as [this creature] enters" or "as [this creature] is turned face up" are also unaffected by Twinflame Travelers's ability.

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.

Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]." Some keyword abilities, such as mobilize (from the Tarkir: Dragonstorm release), are triggered abilities and will have "when," "whenever," or "at" in their reminder text. Replacement effects are unaffected by Twinflame Travelers's ability. For example, a 1/1 Elemental creature that enters under your control "with a +1/+1 counter on it" won't receive an additional +1/+1 counter.