If you buy a voucher online, it is not activated until you enter a park (and you have to do it at a ticket window or guest relations). So you are correct. But the answer for OP is 11:59 same calendar day that you bought it, which means 1 bonus day!
I have a question that I never thought of until just now...What if the park closes very late, like 1am, and you were in on the afternoon of that very last day but you took a break. Could you come back at 12:15, just 15 min past official expiration, and still get in? It seems like you could since it would count as the previous day on a 5 day hopper. Hmm. Just wondering.