When calling adminUpdateUserAttributes to change email address of a user in Cognito User Pools, the attribute email_verified will be set to false, and an email will be sent out to the user with a verification code.
If you want to disable this logic and prevent the email from being sent out, include email_verified=true in the update attributes request, like so:

{
 "UserAttributes": [
  {
   "Name": "email",
   "Value": "new-email@example.com"
  },
  {
   "Name": "email_verified",
   "Value": "true"
  }
 ]
}