Pirelli's tests with Mercedes led to protests from Red Bull and Ferrari during the Monaco Grand Prix, which was won by Mercedes driver Nico Rosberg.
Hembery's warning comes after a series of negative comments from all sides following the pit-stop-decorated Spanish Grand Prix earlier this month and an open war of words between the teams about the fast-wearing tyres supplied to F1 this year.
The tyre manufacturer said the new range combines elements from the 2012 and 2013 tyres to have both durability and performance.
Teams have complained that tyres are degrading too quickly, forcing more pit stops and strategies changes.
Formula One tyres suppliers Pirelli on Monday defended themselves after being accused by seven-time champion driver Michael Schumacher of creating tyres that prevent drivers pushing to their limits.