Jeremiah Smith signed with Adidas to be his brand, so any gear he wears or releases down the line will, barring a termination of contract, be Adidas. Ohio State, however, is a Nike brand. They signed a record-setting deal with the athletic company in 2016 to keep them as the Buckeyes' sponsor for 15 years. Smith will be long into the NFL by the time that deal expires.
So how can this be? It's not as uncommon as you think. The school has its own brand deal, and his jersey, cleats, and on-field gear is Nike. Everything else is Adidas. The brand is banking on his marketability out of college, which is a good bet considering how good he's been in college. They'll pass on the couple of seasons he plays at OSU for the money they'll make when he represents Adidas in the NFL.
This is very similar to two recent college superstars: Cooper Flagg and Hailey Van Lith. Flagg is a New Balance athlete, but Duke is a Nike school. The same thing occurred there, as New Balance only had to wait one season for Flagg to go pro and now, they can reap all the benefits of his stardom.
Van Lith signed an NIL deal with Adidas because she began at Louisville, an Adidas school. She transferred to Nike school LSU before moving to TCU to conclude her career. Her NIL deal with Adidas carried over, though, and so it didn't matter that LSU was Nike-sponsored. They kept her as an Adidas athlete, whom she now reps as a member of the WNBA.
Smith revealed to CBS Sports that he'd been wearing Adidas since he was 10 or 11 years old, so the brand deal was only fitting. A source explained his situation, "Off the field, Jeremiah will be in Adidas product, along with any brand marketing (spots) and individual social media posts." Despite multiple brand offers and OSU's clear connection to Nike, he went with Adidas, and they'll eventually reap all the benefits.