So what you are saying is that if the Contact list on the iPad is not the same or synced with the other devices it defaults to the "real" email address...correct?
No. If it appears as an alias address on 2 of your devices and one shows it as the real address, then it's something with that device. If the Contacts aren't syncing (which I assume it's not since you say iCloud isn't enabled), then maybe it's something with the iPad Address Book listing that is causing this. If her real address is showing there, then it may be picking it up from there. It could be something corrupt in that list on the iPad, or just the way it's listed. So check the AB listing for her name and also look for her address listed separately without her name.
If you reply to that message, what address does that show it going to? And what does she recieve it as?
One other question (and it may sound silly) but just so I'm clear on what an alias actually is; An alias is NOT an actual email address but a "nickname" for your REAL email. It only forwards to the REAL email.
Is this correct?
An alias is tied to a specific email address where you can have several for the same account. However, all aliases and the original address will show up in one mailbox (of your account) because they are actually one. So for my iCloud account, I have my real email address and 3 aliases I use for the account. But all addresses show in the same mailbox. You have to actually view the address in order to tell which one it is sent to.
People receiving email from an alias should only see that address as being sent from.
The purpose of the alias is so that the people don't know your real address, or you can use an alias for different purposes such as one for shopping. If an alias address gets compromised, you can delete it and created a new one. That is not as easy if your real email address is compromised.
And if you send to an alias address, that's the address it will go to. Only the owner of the alias should know it's an alias and it should never get changed to the original in the process. In your case since you know the person, you may have her address listed in the AB as an alias along with the real address and somehow it's taking the original address as the name.