Ceres chill question

So I had ice in the inner chamber that I put in at 9am yesterday. Went on a flight, and got to my hotel at about 5pm and put the entire ceres chill in the fridge. I just replaced the ice in the inner chamber today at 1pm.

I just read on their website it’s not recommended to put the whole thing in the fridge because it won’t keep the temp cold since it’s insulated. Would you keep the milk? There was still a little ice in it this morning around 9am.