To have the plots have a common origin, you need to adjust the ylim() for one or both plots such that the first value for the second plot has the same proportion relative to its ylim as the first value of the first plot has relative to its ylim.
rng(12345)
y1 = randn(50,1);
y2 = randn(50,1) .* sin(2*pi*rand(50,1));
yyaxis right
plot(y1)
ylim auto
yyaxis left
plot(y2)
ylim auto
[l1, u1] = bounds(y1);
[l2, u2] = bounds(y2);
[l1, u1; l2, u2]
%syms p
%(y2(1)-(l2-p))/(u2-(l2-p)) == (y1(1)-l1)/(u1-l1)
p = (y2(1) - l2 + ((l2 - u2)*(l1 - y1(1)))/(l1 - u1))/((l1 - y1(1))/(l1 - u1) - 1);
yyaxis right
ylim([l1, u1])
yyaxis left
ylim([l2-p, u2])
If my calculations are right, the origins of the two plots now align.
