You should ask in Amex forum, because whether it counts as opening a card for 5/24 purposes totally depends on whether it's reported to your credit report as a new bank card account. But Chase forum people are not likely to know that (i've never earn heard term "account manager" in this context before, so I think may be done pretty rarely?), only (some) Amex forum people will know that, and that's why this question belongs (asked in credit report terms, not in 5/24 terms) in the Amex forum, not here.

The only way Chase counts 5/24 (for non-Chase cards at least) is to count the bank card accounts that show on your credit report with an "opened on" date in the past 24 months. So you can tell what counts toward 5/24 or not yourself by examining your own credit report.

Cards you are an authorized user on may count initially, but you may able to get recon to remove them from the count. But I have no idea how "account manager" differs from the much more common "authorized user", because this "account manager" might be an Amex-specific term?