Heat, maybe? The neck might expand and put more tension on the strings, or maybe if you have a tremolo, it might give slightly, during the bending. Then if the strings got stuck in the nut, the unbent string might have more tension when the tremolo system is at rest. I'm just guessing. That happens on my A string of my bass, and the only thing i can figure is heat. I always have to retune my A string by a tiny bit after about 3 songs, then it's good to go for the rest of the night.
As far as built in tuners go, if you can tune your guitar up and your chords sound right, it's working fine. Tuning a fretted instrument is far from an exact science.
Charles