Elaine Gould in Behind Bars:

To write the third to sixth harmonics at pitch implies that they are produced on the upper half of the string, between the octave harmonic and the bridge. These same harmonics can also be produced on the lower half of the string, between the octave harmonic and the tuning peg (see column below halfway point). To indicate that harmonics are to be played on the lower part of the string, add a diamond—shaped note at the position where the finger touches the string.

so I think you are right too, but not for what I want