When eqvivalent transfer function of two systems in series is a product of two transfer functions that describe these systems?
In control systems theory when two systems with transfer functions \$
 H_1(s)\$ and \$H_2(s)\$ are in series equivalent transfer function is
  given as \$H(s)=H_1(s)H_2(s)\$


This is definitely true but why would you consider two cascaded RC circuits as two separated systems!

For example these two circuits are different from each other [One of them could be considered as two cascaded systems each of \$H_1(s)\$ and \$H_2(s)\$ while the other is considered as only one system with a transfer function \$H_3(s)\$

Circuit A:



Circuit B:



In circuit A you cant assume its just two cascaded RC circuits, since the first RC circuit affects the second RC circuit [THE LOADING EFFECT], you need to solve the whole circuit using any circuit theory to come with the differential equation representing the out/input relationship

While in circuit B you can assume these are two separate RC circuits such that none of them affects the other in this case you can do the multiplication 

Circuit A transfere function would be 

\$\frac{1}{R_1C_1R_2C_2S^2+(R_1C_1+R_2C_2+R_1C_2)S+1}\$ 

Whle circuit B transfere function would be 

\$\frac{1}{(R_1C_1S+1)(R_2C_2S+1)}\$ 

Since i have assumed \$R_1 = R_2 = C_1 = C_2 =1\$ which are not practical values but just for demonstration 

Now when examining the unit step response of both circuits you would definatily expect identical responses.

But in circuit A due to the loading effect the capacitor on the right \$C_2\$ is charging through both \$R_1\$ and \$R_2\$ [SLOWER] while in circuit B the same capacitor is only charging through \$R_2\$ [A BIT FASTER]

The unit step response of both of them 



The curve in the yellow [THE SLOWER RESPONSE] represents circuit A while the other curve in pink [THE FASTER RESPONSE] represents circuit B.

So if you think your system is composed of two simmiller systems and its overall transfere function is the multiplication of both of them, you need to ask your self Does each of them affect the other? if so then your assumption is wrong and its a single system that you need to derive its equation.

Also the loading effect is not only in electrical systems, for example in a double tank system you might have the same effect!