If you joined on turn 0 (through the game lobby), you will reinforce on turn 1 and get all scenario units from turn 1+.
If you joined on turn 1, you can reinforce on turn 2 and receive scenario units from turn 2+ only.
...
If you joined on turn x, you can reinforce on turn x+1 and receive scenario units from turn (x+1)+ only.
I think.