From what I can tell from the USGS 7.5 min topo maps, McDowell's Ferry was about four miles down the (Lower Tombigbee) River from the riverfront of Demopolis. The map shows a road which must have once been a railroad grade, given it's as straight as an arrow, leading on the Marengo side to the river opposite the ferry. This road veers west from the Southern RR tracks about half a mile east of the river. So the tracks must have gone to the river at some time; I suppose it was bridged at some point.
But in Civil War Demopolis I'd agree with the CSRR site that the trains were likely off-loaded, freight and passengers put on a steamboat and taken to the next RR terminus, and loaded back on the cars for the rest of the rail trip. Seems inefficient, but there must not have been resources to build a railroad bridge at this point, not only in the Confederacy but for some time after the War. Would they have hazzarded more than one car at a time on the ferry? That would have been just as inefficient, and a good deal more risky.