Generation criterion for dg/stable linear category

Question

I'm looking for the exact statement and the proof of the following statement:

Let $\mathcal{C}$ be a small idempotent-complete pretriangulated dg category over $k$/stable $k$-linear category where $k$ is some commutative ring. Let $\{X_i\}$ be a set of objects in $\mathcal{C}$. The following are equivalent:

1. Every object $X$ can be obtained from $\{X_i\}$ by finitely many steps of talking cones, shifting, and taking retraction.
2. $\{X_i\}$ has the property that $\operatorname{Hom}(X_i,X) = 0$ for all $X_i$ if and only if $X=0$.

Proofs or reference are both welcome.