I only run mine in manual mode and it beeps a few degrees before the target temp is reached and then it beeps again when it hits target temp. I don’t pay too close attention to it anymore but IIRC the number of beeps or the duration is different for the two conditions.
I use a Thermoworks TimeStick Trio for timing, the Anova timer is so poorly implemented I find it to be useless, so I can’t comment on why the timer is starting early.