The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately a measure of that field's tendency to converge on or repel from a point.
In other words, the divergence of J is a measure of how much J change
en la direction given by J itself. Or the solution is the same and there is
no ambiguity.
But i think the ambiguity here is between (a) & (b)
(a) Physically, change of coordinate system should NOT change how fast the charge accumulates in a point.
(b) Mathematically, change of coordinate system does seem to change how fast the charge accumulates in a point.