Anecdotally, nightshade[1] sensitivity seems to be common among people with autoimmune disease and nightshades are one of the anti-recommended foods on the Paleo Autoimmune Protocol, so I think this hypothesis carries some weight.
My personal experience is with Celiac disease and Hashimoto's thyroiditis, and nightshades absolutely destroy me.
[1]Which includes chili peppers, bell peppers, tomatoes, eggplants, and potatoes.
Red tomatoes and certain strains moreso, are very highly acidic. This happens to any and all humans who eat enough tomato. I breed and grow more than 35 heirloom strains of tomatoes, and some days consume many pounds of tomatoes. Through mid season I often get quite a few chancre sores and what you're describing, but I just don't care to stop eating them.
Also to the person above who said that Nightshades bother Celiacs; My grandmother is the only Celiac that I know of and whom has nearly died and been longterm hospitalized back before they could figure out what it was, has never had any issues whatsoever from the Nightshades. They end up being favorite foods of hers. She only has flare up issues with wheat gluten.
As much as your statement on acidity is true, there is also another explanation why this person's mouth is tingling while eating tomatoes, and that could be a histamine intolarence since tomatoes are high in histamine.
My personal experience is with Celiac disease and Hashimoto's thyroiditis, and nightshades absolutely destroy me.
[1]Which includes chili peppers, bell peppers, tomatoes, eggplants, and potatoes.