I think there is valid confusion to be had in interpreting this statement.
Usually, when a statement of "choose either x or y" is made, then the only valid options are exclusively x or exclusively y (None and Both are not valid).
Though, when the statement of "if either x or y then do action" is made, then the action is done with any of three valid options: x, y, or x and y (only None is not valid).
To change the second statement to mean the first, you could say "if only x or only y then do action." The "only" cancel Both as being an option.
Usually, when a statement of "choose either x or y" is made, then the only valid options are exclusively x or exclusively y (None and Both are not valid).
Though, when the statement of "if either x or y then do action" is made, then the action is done with any of three valid options: x, y, or x and y (only None is not valid).
To change the second statement to mean the first, you could say "if only x or only y then do action." The "only" cancel Both as being an option.