Current in RC Step Response circuit
I am not able to understand how current is the getting distributed in RC components after impulse current(t>0+).


Your circuit is non-physical --- you can't have an ideal voltage source applying a step voltage change across a combination of ideal capacitors and get a physically meaningful answer.

In the real world, the behavior would be determined by the internal resistance of the voltage source and the resistance and inductance of the wires connecting the circuit elements. If you want a physically meaningful simulation result, you should include these elements in the circuit model.

In this case, the behavior is determined by the very short but non-zero ramp time you specified for the voltage pulse. If you want to understand what's going on, zoom your plot in on the time between 2.999 and 3.002 us or so. You'll see the capacitors responding exactly as they should to a very quick ramp in applied voltage. To make things more clear, increase the pulse ramp time to 10 or 100 ns instead of 1 ns.

Here I've increased the pulse ramp time to 100 ns and defined all currents to be in the clockwise direction around the main loop and re-done your simulation:



You can see the capacitors charge nearly equally, as they must to satisfy KCL.