Turkish uses <y> for [j] because it's already using <j> for [ʒ]. The romanization of postalveolars in Turkish is very odd; it uses <ç c ş j> for [t͡ʃ d͡ʒ ʃ ʒ], which is a bit odd and inconsistent and produces the very unintuitive use of <c>. Of course, the oddness makes sense when you remember that the Turkish language reformers were Francophiles, which explains the use of <ç> and <j> for [ʒ].
...no??
u is [y]
In fairness I think he maybe switched to discussing [y], because he references Scandinavia and Finland before where [y] is <y>.