It's just to see if you become addicted or not; it doesn't directly control the player and force them to make purchases or anything. If you fail the roll, you either gain Addiction (Mild) or the severity increases; if you go past Burnout, bad shit happens.
Basically, it's like this: When you take the drug, note its Addiction Threshold and its Addiction Rating. In this example, let's use Cram (3 & 4, respective).
After a week passes, if you haven't used the drug, its effective Threshold goes down by 1. If you use the drug again, it resets back to the written Threshold.
If (11 - Addiction Rating) weeks go by without the Threshold hitting 0 at any point, then you have to roll an Addiction Test with a Threshold equal to whatever amount is left over (which will be at least 1).
For example; Firebug takes Cram. The Threshold is 3, and the Rating is 4. That means 7 weeks have to go by without her letting it hit 0 for her to risk being addicted. One week goes by, and she doesn't use again, lowering the Threshold to 2. Then a second week goes by, and now it's at 1. But before a third week passes, she is on a run and uses Cram again. It goes back up to 3 on her third week. Her fourth week goes by, and she's ignoring the stuff, reducing it to 2 once more. Her fifth week she uses again, resetting it again to 3. Sixth week she ignores it, and it's 2. Seventh week comes, and it's at a 1. It hasn't hit 0, so the ("11-4) Week Timeline" never reset, and so she must roll against the remaining Threshold. It's only at a 1 though, so she's probably fine.
All things considered, this means it's not very likely to get addicted unless you have low attributes or are using the drug at least once a week with no breaks.
Some drugs like Kamikaze have Addiction Rating so high that their Thresholds do not reduce fast enough to avoid having to make tests. In the case of Kamikaze, after only 2 weeks you'll have to make a roll, even if you've only used it once in your life. While other drugs can be used once a month with no risk of every becoming addicted.
Is it realistic? No, but there's no good way to enforce something like addiction through pure game mechanics without taking liberties. If your GM thinks its overly complex, they probably think you should never be able to do a drug risk-free, making them significantly more dangerous, and making any user almost guaranteed to become a total junkie. Watch out.