First you did not state what you were using before FTM 2013, so we can not help there, with what the differences are. I do not know what your background is, so trying to define how to ZIP around is an unknown. Like any new program it does take a bit of time to learn the new system and find how to use it.
"If i've cleared the hints on the website, why should i then have to go through it on the desktop!"
As for the hints at Ancestry and within FTM, they are 2 different programs and there for the hints are controlled by each program.
"Does anyone know how to resolve that?"
You must treat them as two different programs and clear the hints in each.