Before I got around to changing my defaults, when I started a new project in ArcGIS Pro, it'd always be in WGS 1984, just like you describe. I'd then go into the properties of my Map and change the coordinate system to the one my organization uses (also a NAD1983 derivative, coincidentally, but a different one), and then make sure to select a transformation from the drop-down there.
Then, as soon as I hit okay on the Map Properties and my map refreshed, I could see it visibly distort relative to WGS 1984 as it applied that transformation.
My bet is that either you forgot to specify the transformation when you selected the projection, or the distortion is happening, and you happen to be in a part of North America (I'm not familiar with 10N offhand) where the difference is slight enough that you didn't notice it'd changed.
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M Reed
"The pessimist may be right oftener than the optimist, but the optimist has more fun, and neither can stop the march of events anyhow." — Robert A. Heinlein, in Time Enough for Love