Re: polishing after claying. This is not needed unless the paint has been marred. After you have finished claying you have a very clean surface albeit covered with lube and small particles of suspended crud. Once this is removed then the surface is ready for an immediate application of wax or sealant which will benefit from the clean surface re adhesion.
Maybe something has got muddled in translation ie the usual steps would be clay, polish and then wax but the polish process is not a necessity.
Clear as mud?
There is a danger in removing anything with clay, be it tar, tree sap or fallout. Small particles are easily pulled off the paint and into the clay but occasionally a larger particle may give rise to a nasty 'squeal' which = a scratch in progress. Unless I am correcting after I prefer to use a solvent to minimise this risk.
Second reason I don't like removing tar with clay is that to remove difficult deposits requires an amount of 'scrubbing' - this pretty much always mars. Often visible as a dulled patch in daylight and def' visible under a Brinkmann.
The extent of this will depend on paint hardness, aggresiveness of clay and sensitivity of the user!
I've used a mild clay (pre-correction) and have marred removing very hard deposits of tree sap. Maybe I'm not sensitive!
Clay - good stuff but needs a bit of care.