No, the first logged in char afaik will get the progress of the current account and will be "named as the one to have unlocked it"
for existing achievements.
The further progress for new achievements is account wide, no matter which char will unlock them. Eiher this unlocking char will be named as the unlocking one then (or maybe the other first logged in char will also be named there).
At least this is what I had understood. Correct me please if this was wrong.
https://forums.elderscrollsonline.co...hievements-q-a
Edit:
Maybe it was changed or a bug what I described above as the Q&A says:
Completed achievements will display the name of the character that first completed the achievement, as well as the date it was first completed. The initial account achievement merging process takes this into account and will auto-update the achievement to display the earliest completion date and character. Tracking individual character progression nullifies the database improvements that Account Wide Achievements bring and isn’t something we can implement without losing those benefits.
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But it definately worked somehow other as I first logged in on PTS a few weeks ago. My first logged in char was all of sudden shown as having completed all the achievments, even on another character (who really had completed that achivements).