Emails from our custom domain ends up in quarantine

Hello CB-MD, 

You have correctly identified the root cause and the first step to solving it, is either to Add the second domain to Microsodft 365 but without getting to the last step which is configuring the DNS records (MX, CNAME, etc), by stopping at this step, the only consequence is that MS365 now knows domainexample.com is a legitimate domain associated with your company.. and this is what you want, after that all your mailflow , mailboxes and all other services will remain with IONOS. 

Then, you can create a rule to bypass Phishing Protection for your second domain, by following the following steps: 
1- Go to the Microsoft 365 Defender Portal: Navigate to security.microsoft.com
2- Go to Policies: In the left pane, select Email & collaboration > Policies & rules > Threat policies > Anti-phishing.
3-Create a new policy or edit the default one.
4-Under the "Phishing threshold & protection" settings, you may find an option to create an exception. Add domainexample.com to the list of domains that are "trusted" or "excluded from spoofing protection."
5-Save the policy.