Asymptotic runtime for querying an interval tree
Querying an interval tree is $O(\log n + m)$, where $n$ is the size of the tree and $m$ is the size of the output. This explains your confusion. Note that there is a trivial $\Omega(m)$ lower bound.

Unfortunately I couldn't find an online proof of this bound, and since there are many variants of interval trees and many different queries, it's best if you tried to prove it yourself for your type of interval tree and query.