No, I got her berserker set without ever taking her to the orc camp. Atugia brought it up to me first when I went to go interact with her one day.
Unfortunately I don't know what triggered it. How far in the story are you? I was decently far in (but that could also be because I rarely interact with her). I also had sub Arona, in case that matters.
For what it's worth I didn't find her berserker set very useful
I am just now at the KM outskirts and lvl 7, I interact with basically everyone except Kiyoko on the reg as part of my RP nonsense. I also have subRona but approaching Tui in the FH, in camp, at Orc Camp, nothing.
That's odd, because it should be procing as long as you've been to the camp and then talk to Tui, as an automatic scene rather than a new talk option. Post a save?
I loaded your save and it seems your Atugia already has the set, you just need to put her in your party and change her armour set, maybe you accidently skipped the talk when it appeared the first time?