There is no real need to temper for primals too.
Ifrit does it because he wants more power (read here, more prayers). Garuda because she is a friggin' psycho wanting her army of slaves.
Titan doesn't care. He just wants to protect his children. Ramuh and Moggle mog XII are the same. I don't think either of them has even tempered their followers, at least in the game's period (maybe before the MSQ took place, but we have hardly a word on these periods)
Shiva hasn't tempered anyone for obvious reasons
Leviathan is unclear. Seems the drowned pirates worship him, but I lack knowledge on whether they were tempered or just decided to worship him after a miraculous escape from death.
Neither Bismarck nor Ravana temper their worshippers, at least as far as we know it (Ravana doesn't need it though, as he is the Queen of the Hive. Bismarck just goes and feeds on floating islands).
Zantetsuken tempers one poor lad at a time though, and Bahamut tempered a dead guy and a primal so far.
as for Alexander, I think he's the same as the others. He just wants to protect his kind, and thus doesn't need to temper them to ensure their loyalty.
I think tempering is more of a last resort thing, either to gain power at all costs (Garuda, Ifrit) or to protect oneself (Bahamut). It also depends greatly on the personality of the primal.
as for the original question, my theory so far is that Alexander is the fuel allowing the sharlayan structure to move. That would also be why he sucks so much aether, as he gives a lot of energy away. You could say the primal inhabited the core of the engine and didn't take a real form like Bahamut did. Destroy the main engine and Alexander is a gonner.
Though it will remain a wild guess as long as we are kept in the dark by SE on this matter. The only word we had on Alexander is "he is awaken". meh.