The meaning of the sign in a phase difference
I believe the terms “leading” and “lagging” can be misunderstood, so I don’t recommend using that terminology. 

Due to the traditional definition of the discrete Fourier transform (DFT), a measured DFT sample phase of zero degrees means the input sinusoid was a cosine wave with an initial phase of zero degrees at time t = 0. So when you measure a DFT sample’s phase to be –90 degrees (your ‘A’ signal) that means the input sinusoid was a cosine wave with an initial phase of –90 degrees which is equal to a sine wave with an initial phase of zero degrees at time t = 0.

Your signal ‘B’ phase of –120 degrees means that input signal was a sine wave with an initial phase of -30 degrees at time t = 0.