The 25-year-old Parker has required points to down both Romanian Razvan Cojanu and Briton Hughie Fury, having won the WBO belt in December 2016.
Joshua felt the Aucklander was degrading his belt with his antics.
"Does he want publicity? Is it a PR stunt?" Joshua told British media.
"What's so difficult about fighting this little kid who's doing press conferences? It's very unprofessional of them - the heavyweight championship is such a respected title to have, but stuff like that takes away from the creme de la creme of the title.
"They need to put their egos aside and stop doing silly things."
Hearn, meanwhile, told Sky Sports UK he'd watched Higgins' slightly disorganised press conference, but still wouldn't agree to a 35 per cent cut.
But he agreed Parker deserved more than 25 per cent.
Higgins considered that progress, having been initially offered a lowball 20 per cent by Joshua's camp, but wouldn't accept less than 35 per cent.
He said the offer was non-negotiable.