Does the damage increase for savage/nimble animal companions include the increased strength?

If an animal companion advances to a e.g. a savage companion (through a feat, most of the time), its stats increase:

[…] increase its Strength modifier by 2 and its Dexterity, Constitution, and Wisdom modifiers by 1. It deals 3 additional damage with its unarmed attacks. […]

Does this mean that its attack damage increases by 5 in total? (3 additional damage + 2 because of the increased strength modifier), oder is the 3 additional damage meant to already include Strength modifier?

The situation is the same with a nimble companion, though I would assume that the answer is the same for both, so I decided to focus on Savage in this question.