Is the complexity of Pollard rho for discrete logartihm really the modulus? so I'm reading everywhere that the Pollard Rho for Dlog's complexity of $g^a \pmod{n}$ is $\mathcal O(\sqrt{n})$.

Shouldn't it be $\mathcal{O}(\sqrt{q})$ with $q$ the order of $g$?
The complexity of Pollard-Rho is indeed $O(\sqrt{\text{ord}(g)})$, but even though $n$ refers to the modulus, their statement might be correct depending of the context. If the modulus considered in your situation is a "classical" modulus in crypto (e.g. $n = (2q+1)^k$ for a prime $q$ and a small $k$, etc), as the modulus will be in general chosen so that ord$(g)$ is big, $n = t\cdot \text{ord}(g)$ for a small constant $t$ so $O(\sqrt{\text{ord}(g)}) = O(\sqrt{n})$.