"Normal" plucking is usually around the sound hole area, which is at 1/4 string length. This gives a strong excitation to the second partial and so it often appears stronger than the fundamental. Tuners of all sorts will trigger on the highest peak and will switch peaks if the highest decays faster than the others. That accounts for the step change in tuning that some tuners show through the duration of a note. Try plucking over the 12th fret if you want to see more of the fundamental.
If you want to pick up on a particular partial, G-Tune allows you to "bracket" the trigger zone using left and right cursors in the spectrum view. The peak doing the triggering is then shown with a red X over it.
AP tuner with the harmonics graph open (View menu) will show you how all the partials vary in frequency over time.
Makes you wonder what "in tune" actually means.
