No, not entirely. Combat damage is dealt in the Combat Damage step (rule 510):
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt.
510.3. Third, the active player gets priority. (See rule 116, “Timing and Priority.”)
510.3a Any abilities that triggered on damage being dealt or while state-based actions are performed afterward are put onto the stack before the active player gets priority; the order in which they triggered doesn’t matter. (See rule 603, “Handling Triggered Abilities.”)
After the stack resolves, everybody passes, the End of Combat step follows, and only then the second main phase.