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I'm confused, is there a way to tell when to follow Game and when to act naturally?
Use the Force. 
But seriously, this is a great question and really gets to the heart of what this process is about. I'd have to say, the newer one is to pickup, the more likely that rules will help him avoid/change past behavior that was hurting his chances of success. But over time, it's good to experiment with replacing these with rules of your own.
Something like the 3 second rule is probably a good one to follow regardless of what system you use, even a totally natural style. It forces you to dive in. Even if it results in you starting the day/night with a crappy set, that will remind you that a crappy set isn't as bad as standing there trying to come up with things to say while she walks off with her friends.
In the end I think the underlying concepts behind the rules are more important than the rules. So you mention don't call twice so you don't seem needy. The important thing here is, don't seem needy. But for newbies, if you tell them this they'll just say, "ok, how do I not seem needy." They've been rehearsing needy for a long time and need a "rule" to force a behavior change.
Rules are training wheels, and eventually you just won't need them because you know how to balance the bike. And that's when the real fun begins.