They work two ways: Restore - meaning you are recovering points, so as soon as you take them (well maybe a round or two later - not specified) you get back what you've expended but to the Restore value. Boosted is points above your baseline level, so the PSI score (and any DMs) are elevated until you use a power then the drug effect drains before your inherent PSI.
And the follow-up I can anticipate (not strictly RAW, but there's enough wiggle room in there for interpretation): If, for instance you are down 2 points and take a standard drug, you get the 2 back and are boosted to +4. But if you took the standard drug when down only 1 point, you get that point back, but still only get boosted to the max for the drug, which is 4. If you where down 7, you'd get 6 back, still be one short of your inherit PSI.
So to answer the question directly: the drug works until you use the PSI it grants. Which means, used defensively against an anticipated Assault, it is actually a fairly powerful drug, even at Standard dose.