In your tutorial on using TTKTopologicalSimplication filter there is an option called Vertex Identifier Field which you guys are suggesting to change the default selection in this case (example)
If I am not mistake, this is because the video was made with a previous version of TTK. The global vertex identifiers are now embedded in the triangulation and dealt with automatically.
The options that are now present may help you with vertex ordering for flat plateaus disambiguation. You do not have to care about the Ids yourself anymore.