My own experience diverges somewhat from the celebrated Tartine experience. Don't get me wrong, I think it is an amazing book and an amazing bakery...it's just that my experience is not commensurate with the book.
First of all, remember that the Tartine bakers who made the starter in the book are, themselves, covered with the natural yeast from working in that bakery - it's no wonder they have a hyperactive starter.
When I decided to make a foray into sourdough, I went with a starter that was basically the Tartine starter. I consulted numerous sources for inspiration, but ultimately found that my starter matured MUCH more slowly than what I saw in the books I consulted.
My starter matured in two stages: (1) where it was able to double in volume within 12 hours of feeding, & (2) where it developed its complex sour smell and flavor characteristics. With daily feedings, my starter finally started doubling in volume after about 2 weeks (I was using equal parts rye and whole wheat to feed it). But it took well over three additional weeks after it developed its capacity to leaven before the flavors in my starter were fully developed. I didn't bake my first sourdough until my starter was 5 1/2 weeks old.
I think that a sourdough starter should be judged more by smell then by leavening capacity. My starter went through phases of smelling like leather, then smelling like wine-y fruit, and finally like acetic acid (vinegary). I baked my first loaf when my starter smelled like San Francisco smells outside a bakery at 5 am - that's how I arrived at the 5 1/2 week mark. And I was going for that bay area sourdough too - nothing subtle. I live in southeastern Virginia - a LONG way from San Francisco - and I swear that my loaves have the uniquely buttery/vinegary tang that I associate with the bay area sourdoughs.
I didn't refrigerate my starter until after 10 or 11 weeks of daily feedings - by that time, I wasn't noticing any perceptible changes in starter smell (and the rising power had been fine since about the 3rd week). Surely the starter would have continued to evolve, albeit more slowly, if I had never refrigerated, but I was satisfied with the taste of my bread by then and tired of the daily ritual and wasted flour. Longer fermentation times using young starters won't generate the flavor that comes with a fully mature starter.
Also, I totally recommend using filtered or bottled water for your starter and for any bread you make with your starter. Starters can smell chlorine like dogs can smell fear. And if you really like your sourdough sour, try using scalded buttermilk for the liquid in your loaf - it adds some lactic acid back to the equation and the milk will help soften the crumb of the loaf.
Good luck and have patience. Great sourdough is worth the time and discarded flour.