For $t$ being the homotopy $t$-structure for Voevodsky effective motivic complexes
when $M\otimes N\in DM_{eff}^{t\le -1}$ ensures that either $M$ or $N$ belongs to $DM_{eff}^{t\le -1}$ (so, we use the cohomological convention for $t$-structures, and  $DM_{eff}^{t\le -1}$ is the class of $0$-connective objects)? Surely, one has to consider motives with rational coefficients here (since $\mathbb{Z}/l\mathbb{Z}\otimes \mathbb{Z}/l'\mathbb{Z}=0$ for $l$ and $l'$ being distinct primes). One can probably construct a somewhat similar example for non-compact (i.e., non-geometric) $M$ and $N$. What can one say about compact motives with rational coefficients, and what about the corresponding question for $DM_{eff}^{t\ge 1}$?