I know while Ar-Pharazôn and his army were sailing to Valinor, Elendil and his sons were getting the faithful away from Númenor, but the one thing I want to know is what were the evil Númenórean civilians doing during this time, does J.R.R Tolkien specify this in The Silmarillion or Unfinished Tales?
There are two groups of evil Númenóreans to consider here.
The first group is those who weren't part of Ar-Pharazôn's army but instead stayed behind in Númenor.
Tolkien doesn't give an account of these, but it's possible that all of the adult men then in Númenor were part of Ar-Pharazôn's invading force. There are two statements in the "Akallabêth" that may support this; first of all that describing those who died in the Downfall:
Númenor went down into the sea, with all its children and its wives and its maidens and its ladies proud.
This implies that those who weren't children, wives, maidens or ladies were off-Númenor somewhere.
Secondly, in the conversation between Amandil and Elendil before the former sailed West:
But let it not be seen that you intend to take many men, or he will be troubled, because of the war that he now plots, for which he will need all the force that he may gather.
If this is the case (and even if it's not) then the evil Númenóreans who stayed behind were most likely just going about their day-to-day business and maintaining the island as a home while awaiting the return of the fleet.
The second group is mentioned in "Of the Rings of Power and the Third Age", in The Silmarillion:
And Sauron gathered to him great strength of his servants out of the east and the south; and among them were not a few of the high race of Númenor. For in the days of the sojourn of Sauron in that land the hearts of well nigh all its people had been turned towards darkness. Therefore many of those who sailed east in that time and made fortresses and dwellings upon the coasts were already bent to his will, and they served him still gladly in Middle-earth. But because of the power of Gil-galad these renegades, lords both mighty and evil, for the most part took up their abodes in the southlands far away; yet two there were, Herumor and Fuinur, who rose to power among the Haradrim, a great and cruel people that dwelt in the wide lands south of Mordor beyond the mouths of Anduin.
These were in Middle-earth, being evil.