If they changed tier in the last 3 months you can:
For a newer club member, click on their recent "Activity" and "View All" near the bottom on their profile page, this goes back 3 months and does record this status change.
To view any tier changes that occurred while a player is a member of your club, again it goes back exactly 3 months, you can see from the club home page, located below the roster, "Member Activity", click "View All" over to the right.
Painstaking and tedious to scroll through the pages but if a player changed tier in the last 3 months, that info is there, in those two places, with the exact date. After that, dunno. :-)
TP