The bottom (pardon my pun) line is that a successful flush requires the body to excrete copius quantities of fluids. Whether the "liquid bowel" effect is caused by Magnesium Sulfate or Magnesium Citrate, you need to be well hydrated before the flush and drink lots of liquids after the flush to rehydrate.
Some of the magnesium is absorbed into the bloodstream from the small intestine, where it causes relaxation of the smooth muscles that control the bile ducts. The same effect on the smooth muscle of the heart is why Mg sometimes lowers blood pressure.
Since the doseage is excessive, some Mg remains in the intestine, causing the body to dilute it with water to rapidly pass it out the bowel. That is what is called "exceeding bowel tolerance", just like Vitamin C.
Whether you max out your blood Mg levels with Epsom Salts or citrate, the kidneys will filter out any unneeded Mg. Strong kidneys retain Mg if the body is deficient in it. Low Mg levels are an early sign of weak kidneys, especially in diabetics.
I found my first several Epsom Salt drinks surprisingly palatable -- probably because I was low in Mg. The final drink was pretty bad. I chased it with apple juice.
Final thought. If you choose to flush, relax and enjoy yourself. If you stress over it, you could cause yourself to retain stones by not "letting go" emotionally.
I find the whole thing rather comical. A bunch of grownups (including myself) eagerly peeking at their poo...