What really happen when user moves fund between Main Account and Trading Account in HitBTC?
This is purely an internal accounting move, no keys are involved.

Their comparison to a hot/cold valid is likely just an analogy. In reality, their application layer (or some middleware) enforces some checks to make sure you can only trade values inside your trading account.

When you transfer funds between them, their internal database accounts are updated. This has nothing to do with blockchains or private keys or utxos. It's purely an internal movement.