Smooth transition between a PTFE tube and the back of a push-fit coupler
The solution might be to countersink the opening at the threaded portion within the tube. There are various angles available for countersinks, although the more common angles are 82 degrees and 90 degrees.

Drive the countersink to the point where the wall thickness is zero, unlike the drawing below showing some material outside the beveled area.



For your purposes, you'd want the steepest angle possible, the 60 degree tool.  If you decided to purchase a countersink, pick a diameter slightly larger than the outside diameter of the wall thickness of the coupler. You could use a countersink of the same diameter as the outside diameter of the threads. 

Center drills are available with 60 degree angles as well:
Amazon specific item


The second smallest center drill listed here has a 1.5&nbsp;mm center point with a 4&nbsp;mm drill point. If your coupling is larger than 4&nbsp;mm, the next size up will not work as well, as the center point is 2.5&nbsp;mm. You'd have to resort to a countersink only.

If you are near a machine shop or have a friend with a mill or even a decent drill press, those resources may be able to perform the countersink for a minimal (or possibly zero) fee.

I have a mini-mill and a collection of countersinks as well as center drills. I found my bag of unused couplers. They are for 5&nbsp;mm tubing and were flat on the threaded end. This is the result after a quick trip to the mill. It appears in the close up that I could have driven the center drill deeper into the fitting, and also cleaned off the swarf a bit as well.