If you are cracking tile and it flexes NO grout will help, you will
probably have to rip it up and start again as no flex should be there.
Bad news but you hired a hack. Get a few Pros out the tile store and
talk to the tile Co, get opinions in writing to confirm this.
Photograph it Video it, and talk to a lawyer. Cork being the problem or
not subfloor is NG. I dont know who is at fault, I hope the cork Co as
they have deep pockets. If tiles crack now wait 5 yrs, they will be
comming loose.