That is not the behavior we observed tonight.
I ran an AL session as a cloud session, with 5 PCs.
At the end, everyone did a "/save".
I closed that campaign, opened a new cloud campaign,
The same player joined the new campaign, and clicked the import arrow, there were no characters for him to select.
As the GM, since I ran both Campaigns, I could see the character and could import them into the new campaign (which was incredibly painless, and much improved, BTW. Thanks!)