Do not take the board's word for it. Draw a random key here, then ask blockstream.info, a public block explorer this site does not run, about each address it controls. Only the address is sent.
Your random key
A brand new key from your browser's random number generator, in hexadecimal, and the four addresses it controls. The key is never sent anywhere.
Each Check button sends one address, and only the address, to blockstream.info, at most one a second.
Nothing drawn yet. The key is made in your browser and never leaves it.
None yet. Each check shows up here with what blockstream.info said.
"0 transactions" means nothing has ever been sent to that address since Bitcoin began. That is what you should see, every time, for as long as you care to keep drawing. It is not a trick of this site: you can paste the address into any block explorer you like.
One key can control coins in several address formats, and the board checks all four that a single key reaches: legacy compressed, legacy uncompressed, native SegWit and wrapped SegWit. Read more in A Private Key Is Just A Number.