Start fresh session:
emacs -Q

C-x C-b
M-x multi-isearch-buffer RET *scratch* RET *Buffer List* RET RET s
(Using C-s several times will search "s" on the two buffers).

M-s e
(Now C-s should keep searching the same string "s" in the two buffers,
  but the string is searched just in the current buffer).