I've said several times there is no difference in the actual build quality or specifications of the lens. It's the same lens. In the past I've seen two versions of a some lens being manufactured in two different countries, with a lesser quality version intended for the international market, but I have never seen Tamron do this with their SP lenses. Their lenses are pretty well built, especially the SP line, and I am fairly confidant they are all coming out of the same factories at the same specs.
To track lenses, manufacturers keep track of the serial number and which market and which pricing structure the lens was intended for. Authorized USA dealers agree to sell the lens for the authorized price and this is how the manufacturer controls the price of their product. But sometimes a dealer will buy a bunch of lenses at a substantial savings on the international market, ship them to the USA and sell them here at a discount. And occasionally those who do might not be so upfront that the lens warranty won't be honored. Usually you will see them marketed as "international version." Buyers simply need to understand this and decide if the savings is worth sacrificing the warranty.
Manufacturers hate the grey market practice and won't repair those lenses or do any kind of warranty work on them. There are no manufactured sanctioned, grey market, back channel, reduced price sales in the USA for which USA warranties will be honored. These kinds of sales operate outside of the manufacturers authorized dealer network, so it's in their best interests to refuse service on them.