Late to the game here, and I'll confine myself to Aquinas: all powers have distinct 'objects', that is - what they are directed toward in some basic way and this is a principled way to distinguish powers from each other. The object of sight is 'color' and hearing 'sound'. The internal sense powers have their own objects too. Dogs have all five external senses and the four internal ones. The common sense unifies the external sense into one phenemonal experience, but the external thing must be present for the common sense to be activated. It's 'object' is the sensible form of the external thing, in a receptive way. Then the imagination makes a 'phantasm', a sense image, which retains that sensible form. Then the other two internal powers, memory and the estimative power (for dogs - for humans this is called the cogitative power) get involved. The external senses and the common sense only deal with 'per se sensibles' - that is the external accidents that are currently sensed: say, some noise or color. The estimative power and memory, by contrast are directed toward, and take as their object, non-sensed intentions (intentiones). These 'intentions' alert the percipient to features that are not available simply to the senses: the noise communicated to the senses thereby becomes meaningful. Thomas will talk about dogs barking, with one dog being able to a) hear another one barking and b) recognizing that the sensed dog is angry. The first (a) occurs by the external sense (hearing) and the common sense. The second, (b), occurs by the estimative power: the dog interprets the meaning of the sound as threatening, attractive, angry, etc, which is content not available to the external senses or the common sense. That estimative power receives the intention, which is not itself directly sensed and the memory stores it.
So, to your actual question: a dog would have sense impression of a human hurting it (perhaps once or multiple times), impinging on its sense of touch. It would feel the hit or prick. This then gets interpreted as pain, which is bad, by the estimative power and stored as such in the memory, and the complex feeling and consequent meaning of the human hitting or poking the dog is stored in memory. The dog can then sense a human and associate that thing (the human) with the pain received. This (the interaction between memory and estimative power (cogitative for humans)) is where what we call trauma would be localized, I think.
While there is no understanding of a universal for the dog, they can (on Thomas's account and others') clearly operate by way of larger groupings. Dogs clearly distinguish between kinds of things (cats, humans, squirrels) and know how to achieve ends (there is clearly know-how), but they don't have a linguistic utterance on this account. So, there's a recognition of the human as a sort of thing and distinguished from other sorts, but not a definition (say, 'humans are rational animals'). They can see triangular things and manipulate them for their own ends, but never arrive at, say, the Pythagorean theorem. So there's no 'understanding of universals' but there is clearly on this account a recognition of groups and items that are in that group.