No, those are the first type. I made a drive dog for driving them using a slot in a face plate. If I remember right I used a 1/4-20 bolt to engage the flat on the mandrels.
Those expanding collets and tapered mandrels make a significant improvement in my work quality.
I dunno about the particulars of how they're made but it looks like a straight matching taper inside the collets to me and if the taper angle matches the mandrel taper then the collet outer surface should remain parallel as it expands. I do know that they hold my pulley castings well and when I'm finished my turned pulleys run as true as you could ask for. That one shown in the lathe is actually too small for the pulley bore so I've got a 15 thou brass shim inside the bore and the mandrel is driven to nearly bottomed out, and I seated the mandrel into the collet with a dead blow swing press* so it's tight.
This thread's focus however is on a new stud for mounting my QCTP.
Thinking about it some more I wonder if the hole quality might be the root cause of the issue that you have with those mandrels and collets. All my bores are first rough drilled and then finish reamed to a straight, precise bore and the collets appear to me to seat properly in them. When I turn that pulley around for counter boring the bottom I'll inspect the shim that I have in there and I may be able to tell if I was only gripping the pulley at the ends or not.
*swing press = hammer☺

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