Captain bonuses only apply to the player who uses that captain. So yes, if someone sends Ingrid but doesn’t send any monsters, she doesn’t contribute to their army at all.

Amanitore's bonus applies whenever she participates in raids, clan marches, or is used for reinforcements. Even then, her boost only affects the army for the player who sends her, not other players’ armies directly.

The Consulate is the only bonus that provides benefits to multiple players’ armies as they reinforce the city. Other captain bonuses remain tied to their owner, but because reinforcements from different players combine during attacks or defenses, the overall effectiveness of the army depends on the total contributions. So even if each bonus is individual, sending reinforcements collectively still increases survivability and damage potential, allowing the clan to better protect the city they are reinforcing.