If you look carefully, you will notice that your bins are not at precisely the same locations. If you instead choose the exact bin locations (instead of just using 100 bins), you'll get what you expect:
H = haltonset(2,'Skip',50+1);
H = net(H,3573*3);
H = reshape(H,3573,3,2);
S = norminv(H);
binEdges = -4:0.1:4;
histogram(S(:,3,1),binEdges,'FaceColor','blue','EdgeAlpha',0.5);
hold on
histogram(S(:,3,2),binEdges,'FaceColor','white','EdgeAlpha',0.5);
legend('Standard normal draws for 1st dimension','Standard normal draws for 2nd dimension')
hold off
Just illustrate it a bit more, here are the differences in bin counts for your method. You see that away from the peak, the values are negative, so the rear bins are fully hidden behind the front bins.
H = haltonset(2,'Skip',50+1);
H = net(H,3573*3);
H = reshape(H,3573,3,2);
S = norminv(H);
hc1 = histcounts(S(:,3,1),100);
hc2 = histcounts(S(:,3,2),100);
figure
plot(hc1-hc2)
