Milk levain

I'm about to try this recipe for sandwich bread http://www.thefreshloaf.com/node/20669/sourdough-pan-de-mie-how-make-quotshreddablyquot-soft-bread?page=1

 I used to use a poolish (with dry yeast) to bake and just left it sitting on the bench till I needed it, which worked well. And I keep my base starter at room temp too. 

But this levain in this recipe contains milk, so I can't just leave it out indefinitely. I assume I can move it to the fridge after a while until I need it? Will that affect the taste? And how long before I use it should I take it out? 

The recipe says to leave it at room temperature for 12 hours. So do I do that first and then move it to the fridge? Or can I just put it in the fridge straight away for like 12 or 18 hours? 

Sorry about all the (probably silly) questions. The actual bread will require a 2 and then a 6 hour rise, so I'm trying to work out the timing to avoid being up baking bread in the middle of the night!