That's how it would work in a tabletop session which is why DM's try to encourage players to stay together. It's boring waiting for other players to finish solo combat, but you both chose to split up, so you face the consequences of said action.
I gues it depends on DM ... but when our group split and then decided to join them on combat, our DM simply told us to roll initiative and let us join right next round. o_O
