The red player can attack the blue player on the 1st day of the week with a purchased reinforcement, but in this case, stacks containing units purchased that week will not participate in the battle (they will skip their turns).
The wording is approximate; the principle is what matters. :)
This, in my opinion, will help avoid annoying situations where the red player accidentally engages in a minor battle with a reinforcement.
In final battles, a reinforcement that serves as a mere statistic (and even disables entire stacks if the red player decides to engage in a final battle but doesn't disband the excess units) should also not provide any bonus, since the blue player doesn't even need to attack it – let's remember the widely discussed situation about the retreating attacker, where the troops cannot destroy each other.
(с) Roger Zelazny