I've read that a Vicksburg undertaker would take down the name of the soldier and bury him in Cedar Hill cemetery.While this wouldn't guarantee that all were buried there, there are supposed to be around 5,000 Confederates buried there.That's probably most of the Confederates who died either in the city's trenches or in the hospitals from wounds or disease.
If Mr. Johnson was in the city or the city trenches when he died, he's probably in Cedar Hill cemetery.If he was one of a few being buried at the time, it's probably a single grave.If there were many needing burial, then they probably dug a long trench and laid the men in it side by side.
Anyway, the undertaker's list was lost and only parts of it are available.Those identified Confederates at Cedar Hill are listed online:
There is a National cemetery in the Vicksburg park, but it was created in 1866 and reserved for Union veterans.I understand that many Union soldiers were reinterred there from scattered battlefield graveyards around the area.
Of those soldiers killed in engagements outside the city defenses (Big Black River, Champion's Hill, etc.) they would have probably been buried wherever convenient be it a common or single grave.As those engagements typically left the Federals in control of the field, it would have been up to them or the local populace to bury the Confederate dead.I'd guess common grave in those instances...again probably a long trench where the bodies were laid side by side.