The leakage spec- in this case 0.01CV (or 3\$\mu\$A) is the product of rated voltage and rated capacitance, not applied voltage. The 3\$\mu\$A, of course, means "whichever is higher" (aka "worse"). So if your cap is rated at 10V/100\$\mu\$F, leakage would be less than 10\$\mu\$A.
SP's rule #1 of data sheet interpretation is:
If a spec can be interpreted in two ways, and one is worse than the other, the worse one is the correct way.
The actual leakage of an electrolytic cap may be much less than the rated value or a bit less. Chances are a higher voltage rated capacitor will have lower leakage when operated at a much lower than rated voltage, but it is not guaranteed, nor will it necessarily last if the capacitor is continuously operated at lower than rated voltage.
The (relatively) long time is, of course, because the initial leakage may be quite a bit higher than spec and it may take some time to drop down to the guaranteed value. This is because the dielectric in an electrolytic cap is actually a very, very thin oxide layer on the etched aluminum plates and it can develop pinholes etc. that are anodized away when voltage is applied.
Here is what United Chemicon has to say about leakage:
Leakage Current (DCL)
The dielectric of a capacitor has a very high resistance which prevents the ﬂow of DC current. However, there are some areas in the dielectric which allow a small amount of current to pass, called leakage current. The areas allowing current ﬂow are due to very small foil impurity sites which are not homogeneous, and the dielectric formed over these impurities does not create a strong bond. When the capacitor is exposed to high DC voltages or high temperatures, these bonds break down and the leakage current increases. Leakage current is also determined by the following factors:
- Capacitance value
- Applied voltage versus rated voltage
- Previous history
The leakage current is proportional to the capacitance and decreases as the applied voltage is reduced. If the capacitor has been at elevated temperatures without voltage applied for an extended time, some degradation of the oxide dielectric may
take place which will result in a higher leakage current. Usually this
damage will be repaired when voltage is reapplied
A strong 'forming' effect of this type is relatively uncommon with modern parts, and seemed to happen a lot more often in olden days when parts were sitting for some time before being used. Maybe the modern electrolyte is better controlled or more pure, or has preservative additives.
Edit: Note @Dave's comment that the units of the 0.01 parameter must be 1/s.