I noticed that in my last send, even though the contact with the same Subscriber Key had changed her email address, the Marketing Cloud has communicated with her using the email on her All Subscriber list. In other words, the email field in the Data Extension was ignored and the corresponding email with that Subscriber Key was used.
Is there a setting where we can change this or do we have to update the All Subscribers list with every import into the Contact Model?
The following setting would be responsible for updating Lists in conjunction with Data Extensions that are used for Triggered sends:
Here is the page that this is contained in within the documentation:
https://help.salesforce.com/articleView?id=mc_es_create_triggered_email_interaction.htm&type=5
From a holistic perspective, maintaining Data in such a way is not ideal. In a perfect world, you would want to use a single source of truth for attribute data (Data Extension/List Fields). Specifically meaning that all things that referenced said attribute data were all aligned to use List Data or conversely all aligned to use Data Extension data.
Attempting to have data be 100% in sync with two objects (Lists/Data Extensions) that are mutually exclusive inevitably presents problems. Specifically, as there is no auto-sync between Lists and Data Extensions, there will eventually be a case where at some point where data between the two objects is not in sync for some period of time. This period of time can be minimized with processes set to match the data up but will still exist. It is also a possibility that data can come from an unexpected place/misunderstood process that updates one set of data but not the other within more complex accounts that have more moving parts.
In most situations where this comes up there is a desire for tracking data which is easily discoverable/available for Lists but less so for Data Extensions. This can still be obtained for Data Extensions however would just require marrying said Data upon the "Sendable Relationship" or "Primary Key" of record with tracking data.
Is there a way for the all subscribers list to not get updated?
No. All Subscribers acts as the master list of all subscriber data, and a subscriber must be on the All Subscribers list in order for that sub to receive email. If a particular SubscriberKey has more than one email address field in a DE, the All Subscribers EmailAddress value will be updated with whatever email address is selected for the particular send.
we only want to send to the alternate email address once.
This is quite simple - just send to the same subscriber again, but make sure to designate the primary email address as the email address you're sending to. Yes, this will update the All Subs email address again with the primary email address, but it will accomplish what you're trying to do: send to alternate email once, and then continue sending to the primary email.
A way around this could be to create a new subscriber for the alternate email address. For example, you could have SubscriberKey_PrimaryEmail and SubscriberKey_AlternateEmail. This unfortunately introduces a potential data management issue, having to account for 2 subscribers for 1 real-life identity. But from a system perspective, it could allow you to bypass the All Subs update.
Best Answer
This is the expected behaviour and you cannot change it. Once you set a Send Relationship in a data extension, for example, Subscriber Key relates to subscribers on Subscriber Key, it will look up the email address from All Subscribers list at send time.
Depending on where your data is coming from, you can set up an automation that will look for differences between your data and All Subs and update All Subs accordingly. Here is an example of how you can set it up if you're integrated with Sales/Service Cloud:
Take a look at Markus' blog for more details: https://markus.codes/2017/07/14/how-to-sync-email-changes-from-service-cloud-to-all-subscribers-list
EDIT
I just found the following article, Profile Center and Marketing Cloud Connect, that says:
If this works as expected, then you wouldn't have to worry about prioritizing Profile Center updates, as they would be reflected in Sales/Service Cloud anyway.