Sometimes I ask sellers if they would like me to hold on to their accepted offer for a few hours just in case another offer comes in. Because once I send it to the buyer's agent, it is delivered and they are in contract. This can happen on a Sunday, for example, when we receive an offer before the open, because many buyers may come through open houses on that day, and they often tour without their agent in tow. Of course, we ask buyers if they are working with an agent because we're not about to tread on another agent's buyer and we respect their existing relationship, should they have it.
Buyers have been known to say they are working with an agent, but when we ask who is the agent, they suddenly cannot recall the name. Still, we try to treat all parties fairly and equally. Which means if they are touring an open house when we've already received one offer, we always let them know that we have an offer pending and will consider all other offers immediately after the open house.
This means generally by 5:00 or 6:00. It does not mean by midnight or by sometime the following day. You can read more in my personal blog today about this at the following link: Making a Contingent Offer When Your Home is Not Yet on the Market.