They love to climb and unlike lots of spiders they are diurnal. Not only do they hunt in daylight but they actually seem to love sunlight. Mine sometimes bask on a leaf.You can probably remove the rock. Just in case the jar falls, the rock won't rattle around and squish the spider. Audax rarely crawl over the ground, they prefer vertical walls by far.
I think ultraviolet light plays a critical role in their lives, especially with such metallic chelicerae. Whenever I paired my Phids for mating I made sure they had good lighting. Make the man spider more attractive.They love to climb and unlike lots of spiders they are diurnal. Not only do they hunt in daylight but they actually seem to love sunlight. Mine sometimes bask on a leaf.
I once had placed a glass vial off-balance. The spider was out and the vial fell and rolled over the baby jumper. Bugger didn't stand a chance...