When configuring Azure AD as the Single Sign On option (Setup -> Admin -> Single Sign On -> Azure AD) for your Customers tenant please ensure you do so through a User account using the customers domain.
The Setup -> Admin -> Azure AD option when selected will claim the domain of the user currently activating SSO, so if done so from a Partner User the Partner's domain will be claimed and block sign in to the Partner tenant.
For example:
If [email protected] switched into the Customer tenant and ran through the SSO process, the partner domain would be claimed under the Customer tenant. If [email protected] signed in and ran through the SSO process, that customer domain would be claimed.
Note: This only applies for the Setup -> Admin -> Single Sign On -> Azure AD option, the SAML option will allow the domain to be claimed to be specified.