I have a 2018 Specialized Crux (the latest carbon frame) with a 12x142mm rear thru axle.
When I place it on the Kickr, it barely hangs on. I have to line up the frame perfectly to get it to rest on both sides, otherwise it slips off. The width of the “hub” on the Kickr is barely wide enough, it is in tolerance by a hair. Once I install the thru axle, the frame flexes to fit nice and tight.
When I install the rear wheel (Specialized Axis), it fits with much less slop.
This is my first carbon frame and first frame with thru axles, and I wonder if this is normal.
Did you install the appropriate width thru axle supports on the Kickr first? There are 2 sizes (142mm or 148mm). From your description , it’s unlikely you have it wrong (since the “wrong” one at 148mm would be wider and be the opposite problem), but I always try to rule out assumptions.
It’s possibly that the 142mm on the Core is a bit more narrow than your wheel hub. Tolerances in manufacturing will lead to subtle differences in fit. It sounds like it is probably OK and not necessarily a “problem” other than the inconvenience of the alignment.