How did you create your import map? I'm asking in case you have transposed a couple of columns or, perhaps, are importing the spreadsheet column that contains successors into the Project column expected predecessors.
(In other words: are you certain your CSV layout exactly mirrors the Project import map?)
In addition, as a quick workaround, how about copy&paste from the spreadsheet into Project. Perhaps, too, that will generate some error diagnostics that point to a solution to your more general situation.