Can an algorithm complexity be lower than its tight low bound / higher than its tight high bound?
If $T(n) = \Theta(n^3\log n)$ then it is always the case that $T(n) = \Omega(n^2)$ and $T(n) = O(n^4)$.
If $T(n)$ is the worst-case complexity of an algorithm, then furthermore its average-case complexity is $O(n^4)$, always.