Jim, your unfamiliarity with south indian tulwars is completely understandable! Compared to their northern counterparts, most south indian weapons are incredibly understudied and subsequently any findings in regards to their typology go largely unpublished (with the huge exception of those from thanjavur, along with the hooded bara jamdadu of vijayanagar, thanks to their codification in writing via a certain Robert Elgood).
My identifying of these riveted tulwars as being tamil in nature stems largely from the work of the late Roy Elvis, who did his best to publish his research in his own book The Hindu Warrior. This book explains his findings in the context of his own collection, which indeed predominately focuses on south india. Roy "himself" (writing in the book) only ever gives a few sentences to each piece, leaving the reader to mostly discern for themselves what else about the item could be evidence for a distinct style. As imprecise as this might seem, I've managed to use the book as something of a reference guide for telling apart different items that are otherwise lumped together online as just generally being "south indian" or "deccani".
As an example of this, indeed, Roy notes that tamil work is generally distinct in its use of sculptural, floral imagery. Typically either the knuckleguard finial, the pommel bud, or both will incorporate the image of a rather squat flower bud - likely intended to be a lotus - though it honestly looks more like a squash to me. This is often coupled with the presence of a more khanda-like stalk or tail at the pommel, despite the hilt otherwise being of a more typical tulwar form. This, combined with a tendency towards riveting the blade in place, is what actually all leads to the tamil attribution, rather than it just being by virtue of the rivet existing in and of itself. Certain tulwar hilts that might be from thanjavur specifically also tend to feature spiky grips, similar to those found on northern rajput swords, buts that's a different issue entirely
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Speaking of a possible connection with Tipu Sultan, one of my examples (the one with the grey background) actually has a mysorean armory inscription on the blade, so it's certainly possible they had an affinity for riveting their blades as well.
The reason why these south indian items are not as common, in my opinion, likely has to do with how most of them were either used up or subsequently confiscated and destroyed during struggles with the british/colonial powers. One of the reasons why south india is generally considered more "developed" than the north stems from the fact that the south was both colonized first and subsequently capable of modernizing earlier - the unfortunate byproduct of this indeed being the disarmament of local traditional militias and their suppliers, meaning again most of these items, willfully or not, were likely destroyed in an effort to comply with more "civilized" and "modern" ideas.
I suppose I should probably note that not all of my attached examples are of tulwar hilts specifically, but my intent is mostly just to prove that these hilt rivets can be found on south indian arms in general, not just north indian ones.