Question: Why does MmaTranslator:-Mma:-PolynomialReduce not work as its name suggests?

According to the documentation of MmaTranslator:-Mma:-PolynomialReduce, this command yields a list representing a reduction of a specified polynomial in terms of a specified list of polynomials. However, 

restart;
MmaTranslator:-Mma:-PolynomialReduce(x**2+y**2,{x-y,y+a});
 = 
                       [         2    2]
                       [[0, 0], x  + y ]

In[1]:= PolynomialReduce[x^2+y^2,{x-y,y+a}](*Mathematica*)

Out[1]= {{x + y, -2 a + 2 y}, 2 a^2}

In SymPy and in MuPAD: 

The output of both is the same as that of Mma; only the result given by Maple is inconsistent with Mathematica's. 

The example above is so simple that the desired result can be found simply by hand. Here is a larger example: 
Given two polynomials poly₁.txt and poly₂.txt, as well as a list of polynomials pList.txt, I would like to evaluate 

# Suppose that one has downloaded these three files. 
poly1, poly2 := fscanf("poly1.txt", "%a")[], fscanf("poly2.txt", "%a")[]:
pList := MmaTranslator:-Mma:-ReadList("pList.txt"):
MmaTranslator:-Mma:-PolynomialReduce((a - poly1)*(a - poly2), pList);

 But its result is just “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], …]”, while when a＝0 it should be “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 0, 2, 2, 3, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], 0]”.
So why does MmaTranslator:-Mma:-PolynomialReduce return a distinct value?