As a user of Aquamail who is using exactly the same setting for one of the accounts, I can tell you that the reason for your problem is not Aquamail but the way you have it configured.
And if you don't believe my word, - the example of your colleague for whom it works properly proves that.
So, your jerk-knee reaction to jump ship is unwarranted.
Here is, I suspect, what you are missing in your configuration: in your case, Aquamail is sending via Gmail's SMTP server, not smptout.secureserver. If your message was going out via smptout.secureserver, there would be NO trace of your GMail address in it, whatsoever, because the message wouldn't experience GMail on its way out.
Here is what you should do:
If the account is configured as IMAP (not Gmail OAuth2):
Long press on the account name (in the account list view) -> Account Setup.
First verify that on your first screen you have "my_username@ourdomain" on the first screen.
Press on "manual". Keep the IMAP settings on the next screen and press on "Next".
On the next, SMTP-server screen, make sure you have smptout.secureserver port 465, and everything else pertaining to that.
(I am ready to bet is that you have Gmail's SMTP there.)
If the account is configured as Gmail OAuth2 (The same would work for an IMAP account):
Long press on the account name (in the account list view) -> Identities
Create (or edit an identity if you created one for your "my_username@ourdomain" address.
In the SMTP server (for that identity), choose smptout.secureserver port 465, and everything else pertaining to that.