Cat puking after eating near new mom cat. Should I worry?

Poor Kilro! It's likely that he could be suffering from a GI illness or possibly eating something rotten rather than be disgusted by your other's cats smell. I will give you a home remedy to try to see if that helps before having to take him into the vet, but I would also caution about letting him near the mother cat and her kittens. Mother cats can be very protective of their kittens around other cats, and they should be isolated while the kittens are very young to reduce stress. Once the kittens have their eyes open and are more mobile (around four weeks of age), then you can let them around Kilro. As for the home remedy, I recommend withholding food for 12-24 hours, then feeding a bland diet of boiled white meat chicken (no bones) in small amounts several times a day for a couple of days. Then slowly add back in his normal diet. If the vomiting continues in the absence of food, he vomits the bland diet, develops diarrhea, stops drinking water, starts vomiting water, or becomes very lethargic, he will need to see a vet right away. I hope this helps!