Thomason discusses the construction in (A.9.1) in his paper with Trobaugh, Higher algebraic K-theory of schemes and of derived categoriesHigher algebraic K-theory of schemes and of derived categories, The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, BirkhaeuserBirkhäuser Boston, Boston, MA, 1990, pp. 247–435. I don't know how he uses it in the body of the paper.
I use it in an essential way to derive a result for all exact categories in Corollary 6.5 of my paper Algebraic $K$-theory via binary complexesAlgebraic $K$-theory via binary complexes, J. Amer. Math. Soc. 25 (2012), 1149-11671149–1167.