Let's see if I can describe this... I cover the analogue cap with my thumb, putting the center of the cap in the center of the last section of my finger (like behind the lower potion of the thumbnail), which means there's a few mm of my finger sticking outside the stick cap. I hold the fingers more or less 45° rotated to the center of the gamepad, and when tilting both analogue sticks towards each other, my thumbs touch, preventing the full tilt of the sticks.

This is a problem for me on PS4 pads, and quite severe on PS3, though doesn't really happen on Logitech F710. I'm an adult, nearing 40yo, my hands have slightly longer than average fingers. This seems like a thing related to the size of the gamepads, I imagine PS1 dual shocks could be unplayable for me.