Slitherine

Two armies, one with +1 initiative and one with +2 initiative, check initiative at the start of the game.
The first player rolls a 4 for a total initiative score of 5.
The second player rolls a 3 for a total initiative score of 5.
It's a tie, so both players dice again.
Are the +1 and +2 initiative modifiers added to the re-rolls, or do the players just use the raw dice scores for the initative re-rolls?

Yes

You add the modifier each time.