It might be that the person is pausing too much before injecting, which makes it worse. Just do a quick jab without overthinking. If the pain comes after, it could be a reaction at the site, but this seems more like hesitation. Alcohol from the wipe not being dry can also sting. Or maybe the needle is getting dull from multiple uses on the vial.
One of the rats I've been treating for a while suddenly started having issues with the injection feeling extremely painful. It took four tries to get it in because it hurt so badly. Everyone else using the same batch has no problems at all. Any ideas why this might be happening?