Think of a transistor circuit as a simple voltage divider.
In a common emitter amplifier, the transistor replaces the low side resistor, R2.
As base current current increases, collector-emitter current will also increase, equivalent to R2 decreasing. Hence Vout falls with increasing base-emitter voltage.
If we put the transistor on the high side (R1), i.e. emitter follower configuration, Vout will increase with increasing base voltage.
Of course, if you can create a device with the opposite characteristics, i.e. increasing resistance with increasing control voltage, then you will obtain the opposite effect from that stated above.
He is asking about phase shift not amplitude! There is very little phase shift through an emitter follower, but the emitter and load capacitance forms an RC circuit which introduces some phase shift. In R is small and C is big the phase shift will cause oscillations.
In a common-emitter amplifier when the input base voltage is increasing it causes the collector current to also increase.
With a resistive collector load, this causes the collector voltage to decrease, thus the collector voltage is 180° out-of-phase with the base voltage.