Your personal tier is only affected by your personal score the last time you participated in CvC.    If you did poorly in another clan you may end up in a lower tier, if you did exceptionally well the last time you will move up  .  Changing clans does not affect that.

Wish i could help but we stay on the last tier and some times that come back to huant us cuz we got peeps on the other team 500k lol thank god this week we will win not so bad )