After the first four races of the season, Pirelli have been in the headlines more than ever after introducing new compounds to encourage overtaking, mix up strategy and create more pitstops.
There have been concerns that the races have become confusing for fans, while some drivers have moaned about having to pace themselves rather than being able to go flat out.
Much of the criticism has come from champions Red Bull, who want the tyres to be longer-lasting and blamed excessive wear for their controversial use of 'team orders' in Malaysia last month.
Hembery said he felt like 'piggy in the middle' and the situation was all "a bit weird really".
"We often sit down and go 'what's all this about?'," the Briton, Pirelli's main man in Formula One, told Reuters at last weekend's Bahrain Grand Prix.
"It's the third year (of Pirelli being sole tyre supplier), it's no different this year than any other year. We've given the challenge, some like it and some don't. They all have the same challenge," added the company's motorsport director.
"In the end we've had the vast majority of teams come to us and say: 'Whatever you do don't change anything'.
"We might - because we have to, and because we see things that as tyre supplier we might want to change - but essentially they are saying: 'Don't change even if you are getting this (negative) media coverage.' So it is rather strange."
Sebastian Vettel won for Red Bull in Bahrain, the triple champion's second victory of the year, but team principal Christian Horner told reporters afterwards that he felt the tyres were still too "on an edge".
"The most vocal team has been Red Bull obviously, and for their reasons," said Hembery.
"The others, if they see one team pushing that way will push against that because they feel there's a good reason why they (Red Bull) want to go in that direction."
Pirelli have been supported by Formula One supremo Ecclestone, who always likes a controversy - or indeed anything that gets F1 talked about - but is also in favour of rewarding strategy and driver skills.
"If the tyres lasted from January to December, there'd be something else to talk about," 82-year-old billionaire Ecclestone told Reuters with a sigh.
"What is good about this (situation) is that it really comes back a little bit to what it used to be when the guys had to look after their brakes and gearboxes and things like that."
The tyres have certainly made a notable difference to the racing this season.
In China, the third race of the season, Red Bull's Australian Mark Webber used the soft tyres for just one lap when he started from the pit lane. In Bahrain, a four-stop strategy was an option for some, with Ferrari's Felipe Massa suffering two tyre deflations in the race.
In Malaysia, Red Bull justified their use of 'team orders' - that backfired when world champion Vettel ignored them and passed Webber to win - by saying they were worried about excessive tyre wear.
Pirelli changed the compounds for Bahrain based on evidence from Malaysia that they might need to be harder, and will go back to Milan to review the data before the European season starts in Spain next month.
Whatever they decide, they will be even-handed.
"We try and do the right thing for everybody, for the sport and the vast majority. We don't want to favour anybody," said Hembery.
"Maybe the engineers and drivers would prefer it that they knew they've got pole and could run away with it...but as a sporting spectacle we know that fans want to have uncertainty."
Hembery, whose company replaced Japan's Bridgestone in 2011 on an initial three-year deal that runs out at the end of this season, expected the situation to calm down once the midpoint of the season was reached.
"The first two seasons were very similar. You get to seven or eight races in and things really do settle down and it'll be the same again this year I'm sure," said the Briton.
When Pirelli came back into Formula One, after leaving in the 1990s, they were asked to make tyres that would help to create more overtaking by becoming a greater part of the strategy.
Making the tyres more of a talking point was also attractive commercially.
"We were asked to replicate Canada 2010 and we are doing what we were asked to do. If you don't want us to do that, tell us and we'll do another approach," Hembery said of the criticism. "But if we do that, maybe it doesn't appeal to us any more being in the sport where you get no visibility.
"That was one of the reasons why the previous suppliers had to go, because they were anonymous.
"We could build the tyres to last the whole race, go to sleep, say we're not worried about any publicity.
"As it is a very dramatic and significant net cost to the business, we have to justify why we are here," he added. "So we need to have visibility, we need to have a profile, otherwise quite frankly we won't be here."
Pirelli have yet to sign a new contract from 2014, although their deal with Ecclestone for trackside advertising has several more years to run, but talks are ongoing.
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