I was able to change the document root of one of my parked domain name using the method described here: Change the document root of a parked domain? by rutiolma. Although, when I tried adding another domain name, it didn't work.
This is what my redirection looked like:
#Modify parked domain directory
RewriteEngine On
Options +FollowSymlinks
#domain1.com
RewriteBase /
RewriteCond %{HTTP_HOST} domain1.com
RewriteCond %{REQUEST_URI} !mydir/
RewriteRule ^(.*)$ mydir/$1 [L]
#domain2.com
RewriteBase /
RewriteCond %{HTTP_HOST} domain2.com
RewriteCond %{REQUEST_URI} !mydir/
RewriteRule ^(.*)$ mydir/$1 [L]
If there is a way to set custom directory for parked domains in cpanel, please enlighten me as I haven't been able to find such a way so far.