you also need to reshape at input. basically you need to:
vector input -> reshape to matrix -> process -> reshape to vector -> output
in your case, you would need to do:
function sys4!(sto, xx)
sto = reshape(sto,2,2)
xx = reshape(xx,2,2)
x = xx[1, 1]
y = xx[1, 2]
z = xx[2, 1]
t = xx[2, 2]
sto[1, 1] = 4.5e-4*x - x*y
sto[1, 2] = z - 1e-14/t
sto[2, 1] = y - 0.02 - x
sto[2, 2] = z - t - y
sto = vec(sto)
return sto
end