I have a rules question. Maybe someone knows the answer.

In the top of the tenth in Monday night's game between the A's and Mariners, Mark Kotsay struck out, then got ejected.

The game was tied after the ejection, but the A's still were at bat with runners on base. The only true outfielder the A's had remaining was Bobby Kielty, but he was the DH. So they had a choice for replacing Kotsay: lose the DH and have the pitcher bat, or put an infielder in the outfield.

I wondered: did the A's have to make the choice of who replaces Kotsay right then and there, or could they wait to decide? If the A's took the lead, they might want to put Kielty out there, to maximize defense and protect the lead. If it remained tied, they might want to keep the DH in the lineup.

The A's ended up not scoring, and Eric Chavez was moved to left field.

I looked it up in the MLB rules, but found nothing. So I'm assuming that the A's didn't have to decide how to replace Kotsay until either (a) Kotsay's turn at bat came up again, or (b) the A's had to take the field.

Am I assuming correctly?