You are correct, the players would lose do to a mill effect before Nekusar, the Mindrazer would do any damage.
Nekusar's triggered ability only goes on the stack the next time a player would receive priority. Before this happens, state-based actions would be checked, and players who were unable to draw would lose.
During the resolution of Minds Aglow, players draw cards. This triggers Nekusar:
603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.
Once Minds Aglow is completely done resolving, the active player gets priority. But before he does, state-based actions are checked.
603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority.
704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.
704.5b If a player attempted to draw a card from a library with no cards in it since the last time state-based actions were checked, that player loses the game.
So not only do players lose before Nekusar's ability resolves, they would lose before they could even have a chance to do something like counter the ability, or cast anything else. Once Minds Aglow starts to resolve, there are no more chances to do anything.