I’ve never worn mine that long or that flat. That said, this is something that will vary from player to player depending on feel, what picks are in use, what the desired tone is. You need to experiment with all those factors to find what works best for you; it will likely not be what works best for me or various other players. But read the suggestions you’ll get; don’t be afraid to try different stuff. Don’t expect to find your answer in a day or two (though you might). Good luck.

Fwiw, here's more-or-less how I wear my saddle brand picks  [with a bit of rotation around the longitudinal axis so they strike the string squarely]: 

And they stay put.... though for some inexplicable reason they also hit too many wrong strings.

Edit: Ooops!!  That's how I wear 'em for what others call Scruggs style.

The purpose of a finger pick is not to add an additional appendage to the end of your finger. The purpose is to add a metal surface to the tip of your finger so that you can achieve the characteristic "twang" of the banjo.

Push the picks farther back on your fingers. You won't have trouble with them coming off, and you'll get better tone out of your instrument.

Picks can be warn as yours are pictured, or they can be worn with pick part closer to the fingertip. Whatever is comfortable and works for you would be the right way for you. If you're hitting a lot of wrong notes, you might try bending the picks closer to your fingertips and see if that helps. If not, you may be trying to play faster than you're ready to play. That will cause you to hit wrong notes at times.

I wear my picks bent and close to the fingertip. I play basically Scruggs type songs.

As far as picks slipping, use the old "lick and stick" way; i.e., lick the tips of your fingers and put the picks on. Acts kind of like a glue. Don't suck the finger, just lick the tips.

I spend lots of time with needle nose pliers, getting my picks just right, from fitting the band to my finger, to positioning the tip very near to the tip of my fingernail. I also like to twist the tips just slightly, to hit the strings squarely.

Re. "lick and stick" I don't need to with the saddlebrand fingerpicks, but I generally do it anyway [force of habit?] and the "lick" does make sliding them on, and rotating them,  a bit easier.   As for my thumbpick, it's a necessity and in my case, if some is good, more is better, and it's from the knuckle to the tip.   

I've also noticed that the effectiveness varies.... sometimes needs a second application.... all I can come up with so far is that the chemical composition might change or there's an imperceptible change in the amount of sweat on my thumb ... though I wouldn't put any doh-rey-me on either of those hypotheses.

When I replied above, I didn’t notice it was in the clawhammer section… or was it moved? Just curious, because we are showing photos that don’t look much like clawhammer to me!

Nope... nothing moved.  I noticed it right after my initial post and edited in an "excuse" of sorts.

And anyhow, thread drift's good, isn't it?  

Oh dear... I posted it in the wrong place! So sorry!