@@Dulset Tarn,
Sighs, Twilight is the Princess of Friendship what do you think Sherlock?
... putting aside the smartass answer the way I personally see it is that for those ponies that 'awaken' as an alicorn once an inner discovery takes place inside. Sometimes it happens unexpectedly, like Cadance after defeating the witch that attacked her village, or perhaps expectantly such as at the guidance of another such as Celestia with Twilight... but both required a realization of one's destiny or purpose and unlocking of magic within. Though with Twilight the catalyst for this was completing an unfinished spell.
What were the echoed words of the spell that led to Twilight figuring out how to finish it? "A mark of one's destiny, singled out alone, fulfilled." And what was the words Twilight wrote? "From all of us together, together we're friends. With the marks of our destinies made one, there is magic without end!"
At least, this is what I have come up with when it comes to what I have been given and consideration what what as not shown. For example the fact that no where does it show Celestia using magic on Twilight before or during her transformation. One would have better argument that Starswirl's spell brought the change, though in actual fact indirectly since the spell only transported Twilight somewhere else, then the princess herself.