Personally I wouldn't normally design on a 1920 artboard because few people have a monitor that large. A range of 1280 to 1440 is much more common for most desktops/laptops.
While your type is a bit large... it's not huge and would fit on smaller screens. If the type on the live site does not match your design, then you should ask the developers about it because I think it has to do with something they are doing, rather than it being Adobe XD.
Keep in mind that it's up to the developer to take the information from XD and then properly code the page. You've provided the specs, but it doesn't mean they have to listen to them.
Adobe Certified Expert & Instructor at Noble Desktop | Web Developer, Designer, InDesign Scriptor