How do exchanges implement their wallet system?

Alright, I’m here again.

To throw more light on the super vague title (I couldn’t figure out a way to make it more clear). I’m working on the part of a system that should handle user crypto deposits in such a way that there would be a parent wallet that controls the funds on behalf of the users, akin to what centralized exchanges like Binance do.

If you’ve noticed, your tokens don’t show up on the blockchain’s explorer when you scan it, but you have a balance on the app. So, from my understanding so far, CEXes use an off-chain system to track balances for users following an IOU strategy.

Now, here is the part that interests me and I’m trying to recreate:

How does Binance (in this case) “instantly” route the tokens to their own wallet from your deposit wallet, without the tokens ever touch yours? I know each user has a different address for, let’s say, Ethereum, so how do they do it?

So far, my idea is to check the token balance of a user’s wallet at certain intervals then sweep the tokens into the parent wallet when there is a balance greater than 0. But there are so many downsides to this, eg, cost of gas.

Any ideas, suggestions, or anything at all would help.