Weird Problem

I use the tuner in my Zoom B2.1U effects before I play. When I started playing my A string was noticeable sharp by a half step. The tuner said it was in tune. I also have a tuner on my headstock that also showed the A string in tune. I tuned the A to the pitch of my E, fifth fret. Both tuners said was flat but ear said it was right. During a break I rechecked intonation and A was sharp at 12th fret. Once I got that adjusted the bass was in tune and both tuners agreed with my ear.

Why did I get a false reading from both tuners initially?

Why did it suddenly go so far out of tune without any action on my part? The other three strings were fine.