When loading it at the same time or even in different time then the server may know based on the IP log or the circuit information.
Correct. So although it may only know the IP address of your Tor exit node and not your real IP address, it can still link all the addresses to each other.
How the online existed blockchain already figured out the wallet address belongs to an offline wallet that is already created?
It doesn't. It has no way of knowing in what kind of wallet that address was generated, or indeed, if that address has been generated by a wallet at all. Every possible valid bitcoin address which can exist already exists, and the wider network has absolutely no way of knowing. For example, if I give you this address:
1MJR9fFWBTN6Zh3EGcYMsFnZzqxzKN6rXhAll the network can do is check the address is valid - it has the correct length, the correct character set, a valid checksum, and starts with a valid network byte. It does not know if I have generated the private key for that address in a hot wallet, a cold wallet, a hardware wallet, or indeed, if I have absolutely no idea what the private key is. Until coins are spent from address, the network has no way of knowing if anyone knows the private key at all.
Incidentally, the address above decodes to the pubkeyhash
DEADBEEFDEADBEEFDEADBEEFDEADBEEFDEADBEEF. I have no idea what the private key is, and neither does anyone else.