Putting in that location does effect the logproducts site as well.
Do you plan to run both sites, not sure why one is a subdomain of the other instead of two primary domains in the same account.
With my service two main domains can be attached in same account with two main public directories which would allow for two different custom 404’s. If a true subdomain is used both names would point to same 404.
Remember a subdomain is just a shortcut to a second directory in the main domain.