  We perform a detailed analysis of the importance of causality within the
strong-field approximation and the steepest descent framework for the
recollision-excitation with subsequent tunneling ionization (RESI) pathway in
laser-induced nonsequential double ionization (NSDI). In this time-delayed
pathway, an electron returns to its parent ion, and, by recolliding with the
core, gives part of its kinetic energy to excite a second electron at a time
$t^{\prime}$. The second electron then reaches the continuum at a later time
$t$ by tunneling ionization. We show that, if $t^{\prime}$ and $t$ are complex,
the condition that recollision of the first electron occurs before tunnel
ionization of the second electron translates into boundary conditions for the
steepest-descent contours, and thus puts constraints on the saddles to be taken
when computing the RESI transition amplitudes. We also show that this
generalized causality condition has a dramatic effect in the shapes of the RESI
electron momentum distributions for few-cycle laser pulses. Physically,
causality determines how the dominant sets of orbits an electron returning to
its parent ion can be combined with the dominant orbits of a second electron
tunneling from an excited state. All features encountered are analyzed in terms
of such orbits, and their quantum interference.
