If you don’t run the tap for ages to top up the jar, it should be around room temperature. If adding that water does cause the thermometer to rise or dip, that’s when you’d add either a bit of cold/chilled or hot water. That’s why I leave a bit of a gap after topping the jar up so I can do that if needed. If the temperature stays within the recommended 18 - 20C, I just top it up with tap water. I’ve only needed to add a dash of chilled or hot water on a couple of occasions and I’ve made dozens of Easyio batches.
You leave the jar out in the kitchen for 10 or 11 hours INSIDE the closed yoghurt maker. Some “flavours” set more quickly but I work on Easyio’s recommended times. I refrigerate it when I’m preparing my evening meal because it’s easier to remember how long it’s been setting. After 10ish hours, it should be set if it’s been made properly. Take it out of the yoghurt maker and put the jar in the fridge. You can eat it as soon as it’s chilled. I’ve had some a couple of hours after chilling it and it was fine but I leave a fresh batch overnight so I can start on it for breakfast. I guess that you could eat it as soon as it’s set but I think it’s far nicer when it’s been chilled.
I hope that helps. If not then I’ll try to answer any other questions that you might have.