I have been putting on talit along with tefilin for over a decade, and I still frequently get the strap of my shel yad tangled in the one of the fore-tzitzit of my talit when I'm winding it around my arm. Once it contacts a tzitzit during its circular motion, they wind together until I notice, and then I have to either unwind them or pull the remaining length of the strap through the talit strings to extricate it.
What technique works well to prevent this tangling from happening? Please indicate in the answer post whether you have used the technique and how well it works for you.