So I used Eiscue to test this, and while doing so I found a shiny! But onto the important stuff.
Eiscue has a special ability called Ice Face, which makes it completely immune to Physical Moves until the ability is broken with a Physical Move.
I used a Wiglett(With higher Atk then SpA) and a Zoroark(With Higher SpA then Atk).
Un-Terastralized Wiglett Using Tera Blast damaged the Eiscue and did not activate Ice Face, meaning it was very much a Special move.
Terastalized Wiglett Using Tera Blast Did break Ice Face, completely negating the damage, meaning it was now a Physical Move.
Un-Terastralized Zoroark using Tera Blast was the same, did damage and did not break Ice Face, very much still a special move.
Terastalized Zoroark using Tera Blast was very much the same too, confirming it as a Special Move.
TLDR: While Unterastralized, Tera Blast is always a special normal type move, Butt when Terastalized and Atk > SpA, Tera Blast will become a Physical Move.
Hope I Helped.