Hi,
It´s a DC supply, thus it´s DC voltage.
Now capacitors block DC current. Thus the "1A" is meaningless for the capacitors.
The job of the capacitors is to stabilize the voltage in case the load draws (short) current pulses.
Especially for didgtal circuits, but also for fast analog circuits you can expect the load to draw currents with high dI/dt.
Now, because the wiring (traces) have inductive character, a fast rising current causes the voltage to drop across the wiring. The voltage at the point of load is not stable, maybe even drops below load device specifications.
So the capacitor acts like a small reservoir of power, just for very sharp change (in the ns range) of currents.
But all currents flow in a loop, thus you not only have to care for low impedance path between capacitor and VCC of the load, but also from load to GND of the capacitor. Here often a solid GND plane is the way to go.
For sure there are applications with (extremely) high ripple current, then you have to select a suitable capacitor.
Klaus