Hi, and welcome to the forum!
Let me just start by saying that I know very little about succulents. I have a pot full of Hens and Chicks out in my front porch that I have seriously done absolutely nothing to ever, and remain alive! It's miraculous really!!!
Having said that, I believe that your planting media may be a little rich on the water retending media.
Now, I DO know about tomatoes! When you withhold water, and then there is an abundance of water, they crack, just like that.
So on a mere hunch, I disagree that what you have there is disease related. I think there is an issue with drainage, an issue with overwatering, and an issue with the compatibility of the growing media with the needs of your plant!
I think a lot of this can be fixed by switching to cactus/succulent mix. Most of the big box stores carry it by the bag!
Hopefully someone super knowledgeable will come along and give you better instructions for care, and maybe some better insight into your problem!
Until then, we look forward to seeing more posts, and again, welcome to the forum!