Is it axiomatic that the Time Hierarchy Theorem holds true in all relativized worlds?
The proof of the time hierarchy theorem relativizes. This means that all the steps remain true if all Turing machines are given access to the same oracle $O$ (for arbitrary $O$). This implies that the theorem itself remains true if all Turing machines are given access to the oracle $O$.

So yes, it is possible to prove that no oracles exist with respect to which the time hierarchy theorem fails.