There are two ways to explain this, the classical way and the general-relatavistic way...

Classically the accelerometer's test mass feels the force of gravity, and this is added on to any inertial forces due to acceleration. So you view its output as the "true acceleration" plus a 1g signal pointing upwards (yes, upwards - think about the chair you are sitting on - it pushes up on you or it would collapse - if you were accelerated upwards (ejector seat?) then that is also felt by you as an upwards force.

So when you rotate the accelerometer but otherwise keep it still, then the direction of this 1g acceleration vector (from the point of view of the accelerometer) changes so it is no longer all in the z-axis direction.

Of course the general-relativity view is that the accelerometer is measuring a true upwards acceleration of 1g (you aren't moving away from the centre of the earth because this acceleration exactly balances out the curvature of spacetime) In general relativity gravity and inertial forces are the same thing.

In practice this means you have to allow for the "gravity" signal and subtract it from the reading to get the "true acceleration". However without knowing how the accelerometer is rotating you can't be certain of the direction of the gravity signal - you need 3-axis gyro to measure this and really measure acceleration. (Actually if you don't know about rotation you can't do anything useful anyway as you invariably want to know about motions in the earth's frame of reference, not the vehicles frame)