The rules state:
Shiloh was a 2 day battle and can only be played
this way. Day 1 ends when the CSA player has drawn all
reinforcements. Whichever player is the attacker in each
engaged position must disengage 1 battle move back
to a friendly position. The USA player receives half his
remaining reinforcements overnight (add to Reserve).
Day 2 begins with a USA turn.
I assume therefore that the CSA player begins and subsequently ends the first day by drawing his remaining 2 cards. Both players then disengage any forces, not as a turn, but just to satisfy the Day 1 ending conditions. The USA player then draws half his remaining reinforcements and starts Day 2 with any necessary Morale Roles.
I would handle it by having the USA cards roll their morale saves, then draw the cards for Day 2.
But that's just me.