The statement means:
Max continuous DC current drain not to exceed 1.5A.
If the current pulses briefly to more than 1.5A it should do so for no more than 10 mS
If it pulses to more than 1.5A repetitively, even if the pulses are <= 10 mS long, the RMS (~= mean or average here) current drain should not exceed 1.5A overall. eg if it pulses to 3A for 10 mS a number of times in a row the off time average should be >= 10 mS in order to keep average drain under 1.5A.
The rise time limit of 10 mA/uS = 10,000 A / second is the MAXIMUM rate at which current draw should change. (Language suggests it may be a minimum :-). ) Ideally this will be arranged in a formally controlled manner.
IF rise time is not formally controlled then the result should be no worse than suddenly connecting a 2200 uF capacitor with ESR = 80 milliOhms across the USB 5V rails.
And how do I apply it?