Here's the proposed law as voted on by California voters in 1994. You can go to page 64 to read it yourself.
From the law, "...if a defendant has been convicted of a felony and it has been pled and proved that the defendant has one or more prior felony convictions, as defined in subdivision(b), the court shall adhere to each of the following:..."
To be pled and proved means the district attorney has to present evidence to the jury that the defendant has committed the prior felonies that would impose the harsher sentences and the jury would have to agree; the jury would have to convict the defendant of violation of the three strikes law.
My "opinion" is based on the text of the law and having first-hand knowledge of the jury instructions that go with a three-strikes trial.
If those references aren't good enough for you then you can look at the following link to California Penal Code 1025(b) which reads:
...the question of whether or not the defendant has suffered the prior conviction shall be tried by the jury that tries the issue upon the plea of not guilty...
I'll take the actual text of the law over your vaunted article in Rolling Stone. Didn't you notice a slightly biased position in the article you read?