I did some digging (pun intended) into the mobile version of my game, and I'm sorry to announce...
It is not safe to progress the hole on mobile.
The overflow issue still persists on this version, but in a rather quirky way. I haven't gotten negative numbers, but instead, my gains are immensely smaller than they should be. Now, keep in mind, I'm F2P and at the end of W7, but not a candy clicker, so these figures are attainable for everyone!!!
As seen in the images, I made a 2 minute claim and got way fewer resources than intended. (I also returned from the web version and got a 55 minute claim, which gave me around 500m. I don't have the image or the exact number, but considering I'm making 112B an hour and couldn't get 1b in 55 minutes is saying something...)
If we do the math, a 2 minute claim should be 1/30th of the afk sheet, or 3.743B (uh oh. Over the 2.14B) How this translated into a measley 23M, aka 0.023B, is beyond me. Regardless, this spells disaster for people who are even just hitting 2B an hour, or 2B in 4 hours, etc...
TLDR: Skilling caverns are not safe on mobile!! Lava, you might wanna fix this, and preferably with something besides a 1B cap...