LUGANO, Switzerland—Giancarlo Devasini, one of the world’s newest billionaires, leads a reclusive life in this Alpine town. He stays in a modest apartment by the lake, strolls the cobbled streets with a black hoodie pulled over his head—and rages about the American rival he believes is trying to kill his business.

Devasini is the main owner of Tether, whose eponymous digital dollar is an indispensable part of the cryptocurrency industry. Tether’s centrality has earned Devasini tremendous wealth and vast influence over the sector, and the support of a top ally of President Trump.