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.
Based on the IP of the broadcasted transaction or anything else like from the input address they can find the master public key and know all address of the HD wallet?
With using TOR connection, there is no way for the owner of the server to know your IP address at all.
But they can know that the generated addresses belongs to the same person. All my confusions were with the response from hosseinimr93. May be this is a misunderstanding. hosseinimr93 is talking about the clear net IP only and I thought he meant both clear net and Tor circuit information as IP.
So now we can fairly say that, the server will know all addresses of an HD wallet will be know from the IP log or TOR circuit exit node information. No?