First off, Tecplot technical support is the first place to go. Chris Idso helped me understand more of what is happening here, and I cannot thank him enough for helping me understand this.
In response to your immediate problem, the settings you have for your STRANDID are incorrect. In Tecplot, STRANDID is used to identify a set of zones that belong to an animation. So in your case, since each zone is a separate solution, the STRANDID should be constant. The SOLUTIONTIME is then used to determine where in the solution evolution the particular zone resides. If you happen to have 100 zones per solution, each zone would have a different STRANDID and identical SOLUTIONTIME, with subsequent sets of 100 zones having incremental SOLUTIONTIMEs and the STRANDID would correspond the zone at the current solution time with the previous solution time.
So for the dataset you uploaded, the STRANDID has to be 1 for the Tecplot animation to work properly (Time animation - which is a bit confusing). The dynamic text issue is then resolved when you use "&(AUXZONE[ACTIVEOFFSET=1]:text). In your dataset, you define "text" as the AUX data for a zone. The "ACTIVEOFFSET=1" tells tecplot to use the first active zone of the set of zones for a particular time step. So, if you set the STRANDID correctly, and use the above dynamic text, you should see the text you desire changing as desired.
If you are talking about one zone at a time in the animation, you might try the following:
Aerospace Research Engineer
NASA Langley Research Center