Blossom End Rot

The reasons for Blossom End Rot

The most common is too much fertilizer causes the plant to grow so fast that the calcium can’t move into the plant quickly enough.

The other reason is there is not enough calcium present in a usable form in the soil/medium.

Calcium is slow uptake all by its self. The calcium available to plants must be present and changed into usable form prior to the plants need to use it. 

Epsom Salt and Tums

Im no chemist, but I think that the sulphate in the epsom salt facilitates (not speeds up) the availability of calcium and other nutrients to be used by the plant and magnesium improves soil quality by providing a hospitable place for bacteria/grubs/etc.

Calcium carbonate in the form of tums should be applied at transplant. Most ground pounders (soil gardeners) apply the finely ground (in a blender, makes it easy) in the hole when the plant is transferred into from another pot/ground etc. The thinking is that by the time the plant needs it, it has broken down into a usable form.