Centroid from calculated root locus is different to the one from MATLAB
I used Octave and I got that the asymptotes goes at -1.4, just as you calculated. You should double check the Matlab result.



I think you might be misunderstanding the meaning of the centroid, it is the point where the asymptote lines meet at the real line, it is not the breakaway point (where the poles leave the real line). Check slide 3 of these notes