installing on hosting where domain is incorrect

My clients domain name has a .com.au domain name but has somehow set up her hosting with a .com domain that she does not own. When I investigated she has added the .com.au domain name as an alias on her hosting account. Note: it is not added as an addon domain or sub domain only as an alias. The problem I am having is that I tried to do an automatic install of wordpress but where it asks you to select the domain the only domain there is the .com so I installed it there thinking it might work and it did install but when I click on the .com/wp-admin it directs me to a completely different url with no access to the wordpress logins.
Can anyone help me as to how she even managed to have hosting and a domain on the hosting that she does not own – I can’t get my head around it.