How does the timing of mana draining compared to ending phases?
Aaron can cast the second Nest Robber and swing with it.

Mana drains from the mana pool at at the end of each step or phase as per CR (emphasis mine):


  106.4: When an effect produces mana, that mana goes into a player’s mana pool. From there, it can be used to pay costs immediately, or it can stay in the player’s mana pool. Each player’s mana pool empties at the end of each step and phase.


So in order for Nick to cast Opt, he must cast the spell before Aaron's precombat mainphase ends. After Nick casts Opt and it resolves Aaron will once again receive priority as per CR:


  116.3b: The active player receives priority after a spell or ability (other than a mana ability) resolves.


Once Aaron receives priority he will be able to cast the Nest Robber as the stack is empty and it is still his precombat main phase (as per CR, emphasis mine):


  116.1a: A player may cast an instant spell any time he or she has priority. A player may cast a noninstant spell during his or her main phase any time he or she has priority and the stack is empty.