Base-change compatibility of the new t-structure

Let $A$ be an associative algebra and consider

$$\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\otimes A\operatorname{mod}).$$

Equip it with the two t-structures described in the source: $\mathrm{new}_1$, obtained by tensoring the new t-structure on the affine-flag category with the usual t-structure on $\bD(A\operatorname{mod})$, and $\mathrm{new}_2$, generated by compact objects $\CF$ such that $\CF\star J_\cla$ is nonpositive in the old t-structure. Base-change compatibility conjecture. The t-structures $\mathrm{new}_1$ and $\mathrm{new}_2$ coincide. The claim asserts stability of the new t-structure under tensoring with an arbitrary associative algebra; its resolution is not given.