find test -newer fileA
finds the test directory as well as the individual files therein, so tar adds test (and all its contents), then test/fileB and test/fileC.
Tighten your find to avoid this:
tar -c -v $(find test -type f -newer fileA) > test.tar
Note that using processcommand substitution in this way can cause issues e.g. with filenames containing spaces;spaces or wildcards; to avoid that, use
find test -type f -newer fileA -print0 | tar -c -v --null -T- -f - > test.tar
(with GNU find and tar), or
find test -type f -newer fileA -exec tar -ccvf -v {} + > test.tar
(assuming you don’t have too many files to archive).