Ok, that’s WordPress’ standard .htaccess file – because all the sites use a common virtual root (think single folder) all domains are using the .htaccess code. Basically you need to rewrite the code to use separate instructions for each domain e.g. this would send a request for newdomain.com to a specific page.
# Internally rewrite new domain home page requests to a specific page
RewriteCond %{HTTP_HOST} ^www\.newdomain\.com
RewriteRule ^$ /specific-page.html [L]