When everyone else does - when the winners are announced.
I can't find an answer originating directly from the Academy on this, but Time covers the 2014 Oscars and had an article which stated:
• A small team of people (about six people, not including Rosas and
Cullinan) split up the ballots so that nobody is counting an entire
category, which means nobody knows how the different entries stack up.
Those subtotals are added up by Rosas and Cullinan [two accountants]. By Friday evening,
the two accountants will know all the winners.
• Though they won’t
disclose how many vote are received, there are about 6,000 voting
members of the Academy. All of the counting is done by hand. “It’s
old-school,” says Cullinan. “It’s as boring as it sounds. You have
lots and lots of stacks of little pieces of paper.”
• All of the
categories are counted several times, and extra if there’s a tie
(which has happened). There has never been a post-awards recount
• The Academy provides triplicates of cards listing each
movie in every category. Rosas and Cullinan put the winning cards in
the envelopes; the losing cards and extras are destroyed.
identical and complete sets of cards are put in two identical
briefcases. This year, PwC has introduced a new style of briefcase —
seen above — which is the first one to bear the Academy’s logo as well
as the accounting firm’s.
• Having rehearsed their blocking on
Saturday, Rosas and Cullinan will travel to the show separately, in
cars with security details. They carry the briefcases down the red
carpet, pausing for interviews, and each take their places on opposite
sides of the stage. As presenters come on from either side, they’ll be
handed the right cards.
This process is backed up in several other places, including the Journal of Accountancy:
Secrecy is paramount. Team members from PwC meet at an undisclosed
location, and each accountant tabulates only a portion of the votes so
he or she won’t know the final results. Only Ruiz and Cullinan put
everything together in the end to determine who the Oscar winners are,
and they commit those results to memory. The winners’ names are not
typed into a computer or written down, to avoid potential lost slips
of paper or breaches of security.
In the final hours before the Oscars
ceremony, Ruiz and Cullinan will quiz each other to make sure they
have accurately memorized the winners in each category. They then will
look through the preprinted cards for all of the nominees, select
those that list each of the victors, and stuff the envelopes. Both
will head to the ceremony on Sunday carrying the correct set of
envelopes. If one gets hung up in L.A. traffic, the other will also
have the results in his or her briefcase. Once at the event, both will
be backstage to hand the appropriate envelopes to the celebrity
presenters during the live event.
So inferring from what both of these articles say, the orchestra find out when most of the world finds out - when the winner is announced. This means they will likely have rehearsed multiple pieces of music for each winner. As @sanpaco says in his comment above, this is certainly not uncommon for a highly professional musical outfit.