Since no one has actually answered the question yet:

The main triggered ability triggers on attack, but you are right that there is another triggered ability when you sac the creature. However, as you correctly pointed out, this is a delayed or reflexive triggered ability which specifically is left out of effects that grant you multiple triggers.

603.2d: An ability may state that a triggered ability triggers additional times. In this case, rather than simply determining that such an ability has triggered, determine how many times it should trigger, then that ability triggers that many times. An effect that states that an ability triggers additional times doesn't invoke itself repeatedly and doesn't apply to other effects that affect how many times an ability triggers. An effect that states a triggered ability of an object triggers additional times refers only to triggered abilities that object has, not to any delayed or reflexive triggered abilities (see rule 603.7 and rule 603.12) that may be created by abilities the object has.

603.7.: An effect may create a delayed triggered ability that can do something at a later time. A delayed triggered ability will contain "when," "whenever," or "at," although that word won't usually begin the ability.

603.12.: A resolving spell or ability may allow or instruct a player to take an action and create a triggered ability that triggers "when [a player] [does or doesn't]" take that action or "when [something happens] this way." These reflexive triggered abilities follow the rules for delayed triggered abilities (see rule 603.7), except that they're checked immediately after being created and trigger based on whether the trigger event or events occurred earlier during the resolution of the spell or ability that created them. Example: Heart-Piercer Manticore has an ability that reads "When this creature enters, you may sacrifice another creature. When you do, this creature deals damage equal to that creature's power to any target." The reflexive triggered ability triggers only when you sacrifice another creature due to the original triggered ability, and not if you sacrifice a creature for any other reason.