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Chemicals are added with the circulation/filtration pump running. When you pour chlorinating liquid in, you do it slowly in front of a return jet. You can see the chlorine being pushed out, diluted and mixed as soon as it goes in the water. Within about 15 minutes the circulation of water that the pump provides causes the chlorine to be very well mixed in the water, if not completely mixed. Generally 30 minutes is about the maximum length of time for complete mixing.
Also, in a TFPC pool with the correct amount of stabilizer (aka CYA, aka conditioner, aka cyanuric acid), around 95% of the 'harsh' part of the chlorine gets tied up as a reserve of chlorinated cyanurates which are not harsh on people, equipment or surfaces.
Many people will also brush the bottom of the pool under where they poured it in, if they think they might have poured it in too fast, or just to be doubly sure. Others will run their pool cleaner for the same reasons, but just pouring slowly in front of a return gets the job done.
About the only way you can bleach plaster with chlorine is by leaving a stabilized (solid) chlorine puck or tablet (trichlor) laying on the bottom of the pool for 10 or 15 minutes. The solid form dissolves, causing highly chlorinated and very acidic water directly against the plaster.
As already mentioned, the sun is the biggest contributor to fading. Pools that are blotchy from the outset are usually the result of plastering problems.
The purpose of inline chlorinators is to provide a convenient delivery method for solid forms of chlorine. Unfortunately all solid forms of chlorine also add either CYA or calcium to the water which accumulates over time, causing problems when CYA or calcium get too high.