Hi,
Inrush current control and delayed start of the circuit are two different factors. Even inrush current be controlled on slow start or slow started circuits. For example:
You drop ONE KILO weight from a height of 2 feet, it will have some some impact at the final surface. Now you drop the same load but hanged with a spring, it will have same impact but will take longer time than earlier, is the delayed circuit start.
Now you want to drop 1 kg weight to the same height but want 1 kg at final destination, so what you do is divide that 1kg into 10 times and the distance into 10 times also. Start dropping that weight and add up that unit weight on every one unit traveled distance, finally when it reaches the destination will not have that impact which will have 1kg in lump sum.
That is INRUSH current control.
Hope I could make understanding.