The sinking velocity integrates the radial (or vertical in a box) velocity of each depth slice only considering regions where the velocity is sinking (i.e. the scalar product of gravity and velocity is positive) and then divides the integral by the total volume of that depth slice. The main code for this is here. I.e. it is not the average radial velocity of only the sinking regions, instead it is more like the average sinking velocity if all material in that region would be sinking (or in other words you could compute the total downward volume flux of material by multiplying the returned value with the area of a depth slice in that depth).
Hope that helps, this code has been in ASPECT forever and I do not think it is used very often, if you need a different quantity we can talk about how to modify it.