I don’t think you are missing anything.
Whilst the Link Mode page in Drafts does make reference to opening web lins in Safari (and a menu on long press of a link?), I don’t believe this is the behaviour any more.
If you take a look at the Changelog, specifically at 5.0.4, you’ll see the following entry.
Change: Use Safari View Controller in-app to open http links in Link mode.
I don’t see any futher reference as to any option to reverse this as a setting and I had a quick scan through them in case I’d missed one.
Maybe Greg made the change as a faster and less disruptive for most users to stay in the app? If this is the case, perhaps it could be proposed as a feature request to have a specification for where the links are opened by default?
It could potentially extend to include other browsers (e.g. Chrome, iCabMobile) in addition to Drafts internally and Safari.