There is a conjecture of Orlov stating that if $X$ and $Y$ are smooth projective complex varieties that are derived equivalent (equivalent bounded derived categories of coherent sheaves), then their rational Voevodsky motives $M(X)_{\mathbb{Q}}$ and $M(Y)_{\mathbb{Q}}$ are equivalent.

My question is whether the equivalence of $M(X)_{\mathbb{Q}}$ and $M(Y)_{\mathbb{Q}}$ implies the partial converse that the rational(!) bounded derived categories of coherent sheaves are equivalent? There is a result of Cisinski and Tabuada that implies that the equivalence of the rational Voevodsky motives implies that the noncommutative rational motives of $X$ and $Y$ are equivalent in Kontsevich's category of rational noncommutative motives.