I’ll give you some guidelines how to verify everything is OK.
You want to check postfix logs and mail headers.
Make sure you have setup SPF-record properly. Beside that it’s recommended to ensure that reverse DNS lookup is working for you. DNS lookup works by PTR records, so to check it, make sure your Droplet is named same as your domain. After that check is there record under Networking -> PTR records.
As it works correctly for Gmail, it’s very high chance that it’s setup correct.
There is a “problem” with
Outlook.com doesn’t trust emails that are sent from IP addresses that didn’t sent emails previously.
It needs some time to build trust with them and Outlook.com Postmaster should help you with it.
You want to pay high attention to Email I send is being blocked or junked by Outlook.com..
Are you sending email from new IPs?:
IPs not previously used to send email typically don't have any reputation built up in our systems. As a result, emails from new IPs are more likely to experience deliverability issues. Once the IP has built a reputation for not sending spam, Outlook.com will typically allow for a better email delivery experience.
And little further you can see the notice:
Note: don't forget to update your Junk Email Reporting Program (JMRP) account with the new IPs. To update or set up a JMRP account, click here.
Try following linked guide, it can help y setup mail server to send correctly to