About Torricelli's law derivation: $p_1=p_2$?

When deriving Torricelli’s law, pressure at points ‘a’ and ‘b’ are said be equal to atmospheric (Figure 1 below).

Torricelli’s law became a specific case of the Bernoulli’s principle, whose derivation uses the diagram below (Figure 2), and requires the pressure at point 2 be tangential to fluid velocity.

_{(source: 4physics.com)}

As a waterjet is formed in Torricelli’s law experiment, atmospheric pressure is tangential only at the start (t=0), and then, at the very end of the waterjet when it’s falling (describing a parabola), until it hits the "ground" (a table, the floor, etc.).

Hence, I would say that pressure at point b of Figure 1 cannot be the atmospheric, also because this point is in the start of a streamline (at t>0).
But as this law has been discovered in 1643, many years have passed since then and there must be something I don’t understand well enough about Pa=Pb. Thanks in advance.