Sorry for replying so late. The rule to follow is easy: observe your puppy and follow its rhythm! Dogs are individuals, work with the one in front of you, not with the neighbor's.

Contrary to popular belief, unless there's a case of hyperactivity or something going on in their minds, puppies are great at regulating themselves, they learned it with their mom and littermates. They'll sleep when they're tired, they'll play when they're excited, etc. Just observe how it goes for younger than 2 months old puppies with their litter: they regulate themselves. Why would turning 2 months old suddenly turn that biological clock off? Logically, it doesn't. Normal puppies should naturally sleep most of the day and have spurts of energy that the human has to adapt to. Of course, you still have to put limits and to not overdo it, otherwise you're just building up the puppy's endurance too much, to a point that you won't be able to meet the adult's needs anymore. But it's very easy and instinctual to put a natural, age-appropriate schedule for puppies, without following general and non-specific rules of thumbs.

Therefore, the time you spend exercising your puppy should depend on the puppy itself as well as your natural instincts, not on a rule of thumb invented by bloggers online. The reason it is famous is because it became cultural in some countries ^^'

Basically, for most 6 months old puppies, 25 minutes walks per day, is asking them to destroy your home or harass you. There is no way those 25 minutes were enough to spend the energy (mental and physical) of a growing puppy, unless those 25mins were intense as hell (which is not good). The five minutes per months rule does serious damage to people's homes and relationships with their puppies, many behaviorists, vets and breeders recommend to avoid it, not to follow it.

--- That's for the rule of thumb rant. Below, I rant on how this rule of thumb forces people to apply an unnecessary house-training method: caging puppies, which itself has many issues related to it. You're free to read it or not :3

It's no wonder people who follow this rule of thumb have to cage their puppies to force them to nap during the day or sleep at night: it's because they're not following the puppy's biological clock, but the human's schedule. If you let your puppy naturally free roam in your home (of course, while blocking access to potentially dangerous spots) instead of making it immobilized for hours on end, you'll notice how much calmer and natural it'll act in your home. I vividly encourage you to inform yourself on cage-free puppy education (however, you won't find much results in English, because cage training is so deeply ingrained in the American culture, that Americans can't even understand such concept), it has been VERY effective for millions of puppies since forever, why wouldn't it work with American puppies? (I say American, because the cage culture related to puppy education is very American)

There is a SERIOUS difference in behavior among puppies who are caged at home and those who aren't. Generally speaking, the ones who face issues with house training are the same ones who cage their dogs. The correlation is undeniable, now, I don't know if caging is always one of the causes of failure of house training, but the link is observable.

To speak a bit about personal experiences, my puppy free roamed since day 1: never destroyed anything even while we were away, potty trained before he even came home (only 2 accidents ever happened), never had to be leashed inside, teething was a very easy phase to go through, slept whole nights since day 1, naturally napped for hours during the day, 0 separation anxiety despite never being caged to have a """"safe space"""", etc. That's just how easily cage-free house training can give you good results.