It's not an unknown or surprising effect, but it gets really complex to make any very specific SWAGs about exactly what's going on in any particular case.

When you pluck a string, you have to pull is sideways a bit, so the tension is slightly increased (hopefully the weight/mass of the string stays constant). This means any plucked note "starts sharp" and as the amplitude of the vibration decreases, the pitch drops. Long arguments can ensue between those who tune to the "attack" pitch and those who tune to the "fadeout" pitch.

When you pluck anywhere except dead center on the string (and sometimes even there) the string will have some "harmonics" in how it vibrates. Each "harmonic mode" acts a bit like a separate little string, that's connected to the other harmonics' separate little strings, so energy can feed back and forth between the individual "harmonic modes." This sometimes leads to audible "beats" that can be heard, and that in fact can be used for tuning. Transfer of energy between individual harmonics of the motion will change the "harmonic content" of the tone as the string motion decays.

The "acoustic impedance" at the bridge and nut, where energy is transfered from the string to the guitar body (to make the noise) varies with frequency, so different of those little "string modes" will transfer a different fraction of the "mode energy" to the guitar body each time a wave slaps the bridge. This, and that the "harmonic modes" are also "trading energy" with each other, also causes the harmonic content of the vibration to change as the string amplitude fades.

So when something changes while the note rings out, it's not surprising.

But if you want the real technical explanations, you'll need to read several very large and boring textbooks, apply a bit of expensive test equipment - and the answer will only apply to the one guitar for which you do the work, (and probably will change when the strings get dirty).

In this particular case, when you strum at the 12th fret, the string frequencies will be at what's "natural" for the place where you fretted. When you release the neck, the frequency content may be out of tune with the octave of the open string, so the existing harmonics will try to pass their energy to slightly different harmonics that fit the open string lenght, which will change the apparent pitch as the energy is transferred to "more efficient" modes of vibration.

Translation of last paragraph: Your 12th fret probably isn't exactly in perfectly compensated position and you're guitar is out of tune - if you're hearing a strong effect.

Advice: It sounds like a neat effect. Work it into your music.

John