You are safe adding an AU to your Chase card as your assumptions are correct. The AU's Open Date will be the same as the primary cardholder's. You are definitely NOT safe doing same with an Amex as it will have it's own Open Date when the AU was added. I won't comment on Citi and Barclays as I'm not certain.
The word "safe" in this context refers to Chase's automatic 5/24 algorithm. Keep in mind, even those AU accounts that are NOT safe can be successfully ignored by Chase during a reconsideration call after receiving an automatic 5/24 denial.