Does the Program take into account the psi factor for frequent load combination automatically as per Eurocode? 

Generally, we create 2 moving load case for each definition, 1st in which psi factor option is checked on and in other load case, psi factor option is checked off.

These psi factor are added directly into their results obtained.

For frequent case, the psi factor moving load case is added to load combination automatically when it is leading and when accompanying, it is ignored as psi2=0.

To verify this, I made a moving load case with EU_ruchrome_nopsi in which psi factor is ignores, rest things are similar to EU_ruchrome as shown below.

Now the model is run and bending moment for one element is observed and compared and it is visible that the psi factors are ignored in nopsi case.

  

Now, while defining the load automatic load combination, add the moving load case in frequent value side to differentiate between psi and nopsi cases as shown below.