My dogs have never reacted to a vaccine, but my once feral cat has.
By the time we got home from the vet, after she received her 2nd rabies vaccine - a 45 minute ride - she was clawing and hissing. Once in the house she ran to our bedroom and hid under the bed for about 12 hours. We keep our bedroom super dark. When I tried to bring her out of the bedroom, with her hissing and trying to bite me the whole time, she squinted her eyes and ran right back to the bedroom.
Both cats were due for their annual vaccines, including their rabies, a few months ago. I discussed it with my vet at that time and she agreed with me that there was no reason to vaccinate again as both cats are kept strictly indoors. If one of the cats gets out we immediately go after them.
We don't plan on having any more cats, even after these two are gone, so this solution works for us.