Laplace and time domain transform confusion with respect to RC LPF
I think you need two suggestions:

1)Pay attention to the fact that a cascade connection of two low pass passive filters is not the multiplication of the transfer functions.
It is true just in this case, with a buffer:







simulate this circuit &ndash; Schematic created using CircuitLab

In your circuit, since the output impedance of the first filter is similar to the input impedance of the second filter something happens in the middle of the circuit.

2)As you can check here:

https://www.wolframalpha.com/widgets/gallery/view.jsp?id=1f9f9d8ff75205aa73ec83e543d8b571

the inverse Laplace trasformation of \$ \frac{V_O}{V_{in}}(s)=\frac{1}{(1+sRC)^2}\$ is not what you expect.