Rav read kriat Shema, donned tefillin, and then prayed. And we conclude that it was theSee inside for why the Rosh disagrees.
messenger who was at fault, for he delayed in bringing the tefillin until after he [Rav] had read kriat Shema, and so he interrupted and donned tefillin so as not to pray without tefillin.
And it is found written in the name of Rabbi Yitzchak za'l, son of Rabbi Yehuda, that the messenger brought him his tallit after kriat Shema and he wrapped himself in the tallit and prayed. And he brought a support to his words from this of Rav, that he donned tefillin between kriat Shema and tefillah, and the same would be true for tzitzit.
Also, see my discussion on Daf Yummy, where I question whether we should really blame the messenger. After all, in the parallel Yerushalmi, this is an explicit position of Rav.