No keys are requested. This is a safe exchange.
I'm not saying your exchange works exactly like I said, just telling others that others Telegram based exchange bots work like that.
I'm not technically well versed with this but IMO, it will be hard for you to convince me to start using this kind of exchange.
Just telling the truth, and I think others will have the same words as I've said unless a well known and reputed exchange will also take a look and adds a feature like this.
Have you taken a look at their website? I think you'll know how they work. Long story short, they provide an all-in-one place for you to exchange your coins via exchanger like Changelly or something similar. You choose the exchange, you deposit to their deposit address, and get your desired coins in return on your wallet address that you provided. It's simple enough but you have to make sure that the deposit address really belongs to the exchange that they listed.