McClements describes Felix's success as "pretty mad"; he is one of around 10 people in Felix's support team, who have recently been fielding interview requests from the likes of the BBC and Japanese television networks.
It all began in 2011, when TPE bigwigs finally gave in to a three-year campaign by Huddersfield staff to add a feline friend to the team. They reasoned that history was on their side: numerous station cats existed all over the country under the previously nationalised British Rail, and a few smaller stops still have domestic pets today. Paddington even has a pigeon-clearing hawk named Pluto.
Felix - initially believed to be a tabby, hence the name - arrived as an eight-week-old, black-and-white ball of fluff that spring. Instantly, her very presence brought smiles to the sour faces of commuters and cheer to staff; beyond that, she has provided comfort to runaway children found hiding at the station, and helped an autistic boy to come out of his shell.
"She was always popular, connecting people, but it was when the Facebook page started that things changed," McClements remembers, sitting in the station's First Class Lounge, which includes a padded cat cushion in the corner.
Initially, when the page started in the summer of 2015, staff had no idea who was behind it. At the time, 'Felix the Huddersfield Station Cat', featured photographs and updates written in the first person, garnering a few hundred likes and no discernible ghost-writer.
Eventually a commuter, Mark Allan, unmasked himself, and said he was happy to let the TPE team help run the group. One of those was McClements, who arrived as a team leader that year, immediately taking to Felix.
"She followed me around a lot back then, especially if I was on my own here. We've always thought of her as a colleague, more than a pet or anything. Then came the uniform..."
To mark years of stellar service (only one person I speak to has ever seen a rodent in the station), TPE promoted her to 'senior pest controller' in February 2016, a post which came with a new, high-visibility uniform and badge. The story went viral around the world.
"I just did it to make people in the office laugh, but I guess we knew it'd be popular," McClements says. In a few days, Felix's page added tens of thousands of new fans, requiring a full team of support staff.
McClements isn't sure what makes Felix such a hit but, in the light of high-earning kitties such as Grumpy Cat and Lil Bub (both internet sensations who have films, fashion ranges and social media followings way into the millions to their names). "People seem to love them, and especially if they can have a personality. And Felix can be quite a diva sometimes, as well as having a hell of a temper."
Felix's book tells the story of her career so far. Proceeds go to Prostate Cancer UK, but McClements admits she may have brought some new passengers in, in the same way Tama, a famous Japanese station cat in the early Noughties, boosted ticket sales on her line by 1.1 billion yen ($10.44m) a year.
"It's probably brought a bit more attention to the network than we expected. It's a real bonus, though, [and] why we do the charity work."
In Huddersfield, Felix has finally woken up. As she pads on to the platform for photographs, passengers pause to gasp. She wears her fame and responsibility with impressive insouciance, posing uniform-free.
"She's a pro at this now," McClements says, watching proudly. "She knows what they want." He's right. After 10 minutes, Felix disappears to hide under a bike rack. Well, you can't just give it away, can you?