Unauthorized Installation of AT&T-Cloud-Backup

So, to be clear, you have a completely different Apple/icloud ID from your husband, and you’re sure that he does not know your Apple credentials, correct?  Are you on the same AT&T account as your husband, because your first sentence suggests that you are.  If that’s true, then you need to get your own account.  Also, are you sure that texts/iMessages aren’t being mirrored to his phone through your phone settings?

I have to agree. It's far more likely that he has accessed your Apple ID. All he has to know is the related email, and be able to guess what sort of password you would use. 

Simplest fix is for now to turn off iMessage.  

Change your Apple ID password. You might even want to change the email related to your Apple ID just for extra security.  

Also two-factor authenticate your Apple ID. 

Make sure that your iCloud back up an Apple ID are yours loan and not shared 

If you did have an AT&T message is back up and sync, it still is a passworded program, And the only way to use it or sign up for it is with possession of the phone because it has to be authenticated on the phone itself. . So I very much doubt that that is what's happened, instead I believe it's your Apple ID that's been compromised

Thank you both for taking the time to respond to my question, I really appreciate your help. To clear it up. Yes, I have my Apple ID separate from my husbands and he does not know my password or any of the information pertaining to anything with my Apple account.

The AT&T account was opened by him at the store alone and he also purchased my phone at that time and had it in his possession until I got it from him. I did not realize that allowing him to do the initial set-up of my phone when he bought it while opening our wireless account at the AT&T store, that he would be able to install  AT&T cloud back up. I had no idea that existed. Do you know how to detect if the AT&T cloudbackup program is installed on my phone? Since he did have my phone and did the initial set up he would’ve been able authenticate the AT&T cloud backup service as you said would need to be done. I just can’t figure out how to detect it on And without the primary account holder password that AT&T requires when you call to make changes on a wireless account I don’t think I could have them help me either

If you do have AT&T messages back up and sync, or AT&T cloud on your phone,  log into it, turn it off, and delete it. 

And get your own account. Do a transfer of billing responsibility off of his account and open your own

Ultimately, you may have to bite the bullet and get your own account.  If he won’t let you off his account, that means getting your own phone number.  There are limits on what you can do when you’re not the account holder.