Multiple WP in sub-dir's, each a unique domain

Using Dotster. (waits for moaning to die down)

So I believe this is Cpanel, though it doesn’t seem to say so clearly anywhere.

Hosting package includes 5 “webspaces” which I understand to be 5 physically separate locations on servers.

Within one webspace I want to have several unique domains. This works fine if I am just using HTML sites. But I want (probably) all of them to be WP in future.

So, the domain names are pointed to sub-directories to contain each domain’s website. For now I am trying to get just 2 domains to work like this.
There is no website or domain pointed at the root of the webspace.

I install WP in each sub-directory, everything says OK in sync, etc.

BUT – when I go to the WP admin URL for “Site 1” it comes up fine and lets me log in.
When I go to the WP admin URL for “Site 2” I get a generic placeholder page from the hosting company.

Is this a WP related problem? Is this a non-acceptable set up for WP? Or should I be talking to (gasp) Dotster?

Thanks, sorry if its something stupid, WP is new to me and multi-site set ups have never been a problem with sites made in an HTML editor and uploaded via FTP.