The symptoms you are describing are actually competely normal and are built into the shift parameters. If you search through this forum and go back about 6-12 months, you will encounter multiple threads describing this perfectly. Sadly, the only way to get rid of this hesitation is to get a tune (Which I would highly recommend BAMA).
As for Yankefan, that is NOT normal. Take it to the dealer immediately and get it fixed.
Unfortunately a tune can result in warranty work denied! We shouldn't have to resort to aftermarket to make the car work properly. I had a 2005 Mustang GT automatic and it shifted MUCH better than my 2012 does. I love everything about this car except the lame shifting - flare from 1st to second, slow downshift when I hit the gas, and not downshifting when I am coming to a stop. Dealer says it is all "normal", no fix from Ford.
2015 Mustang GT 50 Year Anniversary, Ruby Red coupe. Staggered fit 19 inch wheels from American Muscle. Front tires are Sumitomo 245/45 19, rears are Sumitomo 275/40 19. Sound tube deleted, resonator deleted, replaced with h-pipe, Bama tune, custom sub woofer with Rockford Fosgate P3D4 10 inch subwoofer driven by and Alpine MRV 500M mono power amp. Replaced Sync 2 with Sync 3.