The timing I believe is around morning when the Terraria NPCs arrival which requirements are met (I'm not sure about respawning). But has anyone been keeping track on the exact time they arrive?
If its daytime it will usually will have 1 NPC every 2 Minutes.
If its night time the NPCs will not spawn.
However it also affects if a bloodmoon has happened. If a Bloodmoon has occured the NPC will not spawn for the first 10 minutes of the day after.
Officially Day starts 4:30 game time