Need a quick answer... Starter almost too active

Photo: Atleast tripled if not - more, and just starting to break the surface.

So I had some 100% whole rye Levain @ 100% hydration leftover from last week that I stored in the fridge after peaking. 

Last night I fed 50g of this levain with 50g water + 50g khorasan flour as the first feed of two to change it into a khorasan starter. 

Now I know that khorasan is quick but it peaked in 3 hours! after a week in the fridge to-boot. Now I know that just because it has peaked it doesn't mean it doesn't have any juice left but was bedtime and thought it might be stretching it a bit to leave it all night. So I put it in the fridge. 

Tonight I took it out for the second feed (plan on baking tomorrow) and in order to time it well I whittled it down to very little and gave it a big feed. Must have been at least a 1:3. I also thickened it up to around 80% hydration to further slow it down. However within 3 hours it has peaked. 

Now I'm off to bed very soon so do I refrigerate or do I leave out under the assumption there is still a lot more time and food despite appearances? 

If i refrigerate would it be ok to use first thing in the morning. As a rule I only use mature starter from the fridge within a few days and must be mature when refrigerated. Is my starter mature now? 

P.s. It has grown within the last 20 minutes and now has more holes on top. It is crackling when I put my ear to it and the smell is good! I'm refrigerating it. Will use straight from the fridge tomorrow morning.