OK, I looked into the round insert turning tool holder I have, and here we go:
My toolholder is 10mm square and is designed for 10mm round inserts with 11° relief angles. The differences between mine & what
@ltlvt purchased are the "P" vs "C" (11° vs. 7°) and the "1010" vs. "1616" (toolholder dimensions). The differences between the inserts should only be the "P" vs. "C" again (relief angle). Everything else should be the same, but:
My holder came with an M4x10mm screw, and the table on the eBay listing agrees with this:
and the M4 screw fits the hole in the insert perfectly:
ltlvt's holder is a little different; the lettering on the side indicates that the correct screw is an M3.5x10, and also takes a T15 driver (like the M4):
I have some M3.5x8 screws, which will fit my inserts, and while they don't fall through, they sit deeper in the insert than normal.
There are issues with the Amazon listing:
The Holder Specs Photo shows a T10 driver, not a T15 (T10 will "work" with an M3.5 but it's really too loose):
The Insert Specs Photo shows that the inserts do not have a very pronounced chip breaker, but more importantly show the incorrect relief angle (11° instead of the "C" 7°) and thickness (3mm instead of the "T3" 3.97mm):
Due to all of the issues and discrepancies with what
@ltlvt purchased (twice), I recommend that both holders be returned for credit (item not as described and the listing says "Free Returns"; Amazon will try to do a replacement, but the Return Page will allow you to get a credit instead) not replacement and he look elsewhere for a 10mm round tool holder.
I checked on eBay, but unfortunately the three listings for SRDCN1616H10 holders in the U.S. all use the same photo's as the Amazon listing (probably would be drop-shipped from Amazon to you).
There is a listing for the 11° relief angle version in the U.S. if that would work for you (looks like the same holder that I have only 16mm instead of 10mm).
I did find one in China (they are all from China, but this one is still there and it will take a couple of weeks to get to Texas).
On a side note, Amazon doesn't know anything about items like these other than what their sellers tell them, and Amazon also has the same issues as other suppliers. A couple of years ago I ordered some +2.5 safety glasses and received +2.0, clearly marked as such on the package. I did a return with replacement and the replacements were the same – apparently whoever filled the bin put the wrong item in it so everyone who wanted _2.5 got +2.0. I didn't wait for them to get it straightened out and ordered a pair from Grainger. for a couple of dollars more.
Good luck,
Charlie
I did just find 2 Carboloy button insert holders out in the garage though . 
Either the inserts are wrong for the holder or the screw is the wrong size .
