I've used Tandy double-cap brass and nickle plated rivets for 10 years. I've had very, very few problems with them and 99% of those were me.
1/8" is too tall. 90% of the time, the post is going to lean or shift to the side. Especially if the hole is too large. The hole should be just big enough to let the cap set all the way down.
1/16" is the recommended height for all rapid and double cap rivets to the best of my knowledge.
To use a "too long" rivet, I use a pair of fine, flush-cutting cutters to trim them to size once put into the leather and then reshape the post with them as well. I've had maybe 5 failures in those 10 years that I am aware of.
I've also set them with and without the concave base. I've never seen any difference other than visual - flat base vs domed base.
All of this being said, I recently bought the Goldstar press and dies. I have set countless double caps that were at least 1/8th" above the surface and had zero posts leaning over. I leave the dies in all the time and just grab it, set it on the bench and go. Just be aware that the Goldstar double cap dies are marked in mm size and Tandy rivets are all mis-sized. I beleive the mediums are marked as 7mm and are actually 8mm. So you have to buy a die size larger.
Their Line 20 snap dies are not cut to fit the Tandy snaps either. They fit everybody else's, per the guy at the store.
Good luck