Yes, it is true that having multiple domains in the same hosting account present some peculiar Rules that must be followed so as not to fall into disfavor by the Search Engines, but they are not difficult to comply with at all. Some posts have already been made that clearly demonstrate the same concerns that puzzle you, and reviewing them may help provide some understanding. Here are the basics:
1. Do not create multiple sites for the same business, as this invariably creates "duplicate content' and is one of the most serious SE offenses that will result in severe penalties. Some have tried to skirt the issue by creating websites with as much as 60% all-new and unique content (a much less degree of "uniqueness" than even required page-to-page within a single site - the Rule is each page must be at least 80-85% unique), but eventually discovered that they were penalized by the Search Engines on ALL sites nonetheless, the majority of them penalized permanently (on each Domain, not website).
Multiple Sites For Same Business? 2. Do not create links between sites in the same hosting account, whether or not you feel there is significant relevance between them or not. Invariably also, such practices are clearly "interlinking" in the least and "bowling" in the worst, and all such linking strategies will be evaluated as "Black Hat SEO" methods by the SE's immediately, especially since the sites are withion a single hosting account and share an IP address.
Linking Between Sites | Link Types | Sites Penalized | Black Hat SEO to Avoid 3. Do not create 301-redirects, but
rather choose one of the following 2 methods:
A. At the Domain cPanel, FORWARD the Domain that is deemed "lesser" to your Main Domain, for in this way there is not negative SEO affect upon any domain at all, since all metrics are attribute to the Destination Domain, not to a Domain that has no site or other characteristic associated with it;
B. Create a single-page "referral" website for each secondary Domain, inviting visitors to proceed to your Main site. Also on this single page portal, you can have some AdSense placed to captialize on the potential divergence of traffic to earn some revenue. This minimal content and a single "outbound link" to your Main website is not enough to create a violation, and by the addition of AdSense, you will contribute to a more dynamic Content aspect that will diminish the fact you are promoting an outbound link yourself.
* If your Domains are generic, normally occurring terms or relevant words-based, forwarding the to a Main Domain if not in use is a smart way to "activate" them as far as Search goes (as they will come up if the User types in similar words or phrases) and can then provide an additional degree of referring traffic organically to your site.