IMO:
The entire contents of the dashed box are under vacuum if flow is established with some velocity ##v##.
Start by applying the "Energy Equation" between positions 1 and 2 (under the assumption of steady flow - not time varying). 1 is the free water surface, and 2 is located inside the pipe at the free water surface. The tank is assumed to larger that the pipe. It doesn't have to be, but it makes the result more obvious.
$$ \frac{P_1}{\gamma} + z_1 + \frac{v_1^2}{2g} = \frac{P_2}{\gamma} + z_2 + \frac{v_2^2}{2g} + \sum_{1 \to 2} k \frac{v_i^2}{2g} $$
##P_1## is 0 gage
##1## is the elevation datum ##z_1 = z_2 = 0 \rm{elev.}##
The tank is assumed large as such ##v_1 \approx 0##
The last term is a generic head loss term for any real (viscous flow) it is always positive for any established flow in the system.
By continuity (constant pipe diameter) ##v_2 = v_i = v##
We find that the pressure inside the pipe at ##2## is given by:
$$ \boxed{ \frac{P_2}{\gamma} = - \left( \frac{v^2}{2g} + \sum_{1 \to 2} k \frac{v^2}{2g} \right) }$$
Thus, the pressure at ##2## is necessarily at vacuum (and is it atmospheric just below it).
We can do the same analysis for ##2 \to 3##:
$$ \boxed{ \frac{P_3}{\gamma} = \frac{P_2}{\gamma} - \left( z_3 + \sum_{2 \to 3} k \frac{v^2}{2g} \right) } $$
It should be apparent that ##P_3## is the peak vacuum pressure in the system. Also, ##3## has a limit, as the pipe rises higher and higher, the pressure ##P_3## is approaching the vaporization pressure of the liquid. Cavitation will occur at some maximum elevation for the siphon at ##z_3## and the flow will be interrupted as the bubbles expand.
The vacuum is created by the adhesion
@hutchphd is pointing out. You are priming the siphon with vacuum conditions, then water must "fall out" pulling on the water next to it to maintain those vacuum conditions once "manual suction" is removed.
Merlin3189 said:
The air pressures may be the same, but presumably the liquid pressures differ, else why would the water come out?
The pressure at the surface ##1## and the fluid jet are the same almost immediately after the jet exits the pipe. The pressure change propagates at the speed of sound in the fluid.