The honest answer is that it depends on the facility, and both answers you are hearing have some basis in reality.
If you report by 8 pm Saturday, the clock on your two days starts running from that point. Strictly by the math, two days from Saturday evening lands you at Monday evening. But facilities do not always work on strict arithmetic, and weekend release schedules are often driven by staffing rather than precision timing.
Some facilities process weekend releases on Sunday evening to clear beds before the new week starts. Others hold everyone until Monday and process releases during normal business hours when the full staff is on duty. A few go strictly by the hour and will release you when the time is actually up.
The most reliable thing you can do is call the facility before you report and ask directly. Ask what time releases are processed for weekend sentences and whether there is a standard checkout time. That conversation takes five minutes and gives you a real answer instead of guesswork.
When you report on Saturday, ask the intake officer the same question. Get a name and write down what you are told. That way if there is any confusion on release day, you have something concrete to point to.
Plan for Monday to be safe, and treat anything earlier as a bonus.