I understand that quasi-linear functions have a general form
$U(x_1,x_2,...,x_n,y) = f(x_1,x_2,...,x_n) + y$
and that for a quasi-linear function, the income effect with respect to the other variables of the function ($x_1,x_2,...,x_n$) are all $0$, i.e., income has no effect on the consumption of those goods. I also read online that a if a preference is quasi-linear, then indifference curves are parallel.
However, I came across this function, $U(x,y)=e^xy$, where the income effect with respect to $y$ is $0$, when the price of $y$ changed. Is this also a quasi-linear function, since IE is $0$? Plotting the graph of this function, I see that the indifference curves are actually not parallel.