Hi @Anonymous,
Welcome to the community! 
There might be something wrong with the takeoff/tap family. It was possibly changed/loaded into your project by someone else? I attached the default metric and imperial rectangular takeoff/tap for you to reload/overwrite.
The reason for me stating that is that I tried to mimic your problem and I came up with standard graphical representations which you would expect.
"...fact that the tap technically is in the duct a slight amount so it fools the graphics..."
Standard way in which it would connect, so I don't think it has anything to do with the slight cut into the duct runs.

"...if there is a reducer on the diffuser, that shows through everything else, if there isn't, then the rectangular portion of the tap shows."
Here is some of the graphical representations below, tested with both a reducer included from the diff and without.
Not under larger Duct Run, MEP Hidden Lines Turned Off:

Under larger Duct Run, MEP Hidden Lines Turned Off:

Under larger Duct Run, MEP Hidden Lines Turned On:

Everything is pretty much what you'd expect. Did you possibly change any of your Graphic Overrides of your Ducts, mainly the transparency?
The image below shows everything to be 100% transparent, but you should clear those overrides. (If present for testing purposes).

So, if the attached Families do not resolve your issue, you can attach a partial part of your project which can then be investigated, or your family. The partial project would be better.
I hope this helps! 
Rudi Roux
MSc | Digital Engineering Manager
LinkedIn
Revit Mechanical & Electrical Systems 2018 Certified Professional | Revit MEP & Architecture 2015 Certified Professional
AutoCAD 2015 Certified Professional | Autodesk Building Performance Analysis (BPA) Certificate
If this post resolved your issue, kindly Accept as the Solution below. Kudos are always welcome ⇘