The thing I am saying that there is no way we can have an ideal phase transition. A phase transition means there is a point with a specific temperature and pressure where the two phases are in perfect equilibrium and there is no energy needed to change phases. In real life this doesn’t happen. you have that extra barrier, the “free energy barrier”, that needs to be crossed before water can begin solidifying into ice. The sample that was initially warmer crosses this “free energy barrier” more easily than the colder sample, so it actually begins freezing first. However, the colder sample will be the first one to freeze completely, and will always have a temperature lower than the sample that was initially warmer. There is no contradiction of any physical or thermodynamic laws anywhere here.
The important thing to note is that the colder sample will indeed be the first one to solidify completely, so I’m not arguing that it won’t be the first one to freeze. The warmer sample will however be the first one to start freezing. In other words, it will be the first one where you will see ice crystals form.
And I’m saying that you are wrong under most conditions that most people are considering. Read the column. Even for the case in which you were right, your primary cause is wrong. In that case, evaporation of the warmer water was the primary cause.