As in many kids' movies, the world of the children is different from that of the adults. In this case, Mary comes across as a friendly-but-strict nanny to the adults. The children initially also see her this way, but they soon learn that she's a very interesting person.
The "spoonful of sugar" scene helps illustrate this point. Mr Banks will really only hear that Mary made the children clean up their room. But only the children know that Mary uses magic to do so.
The way Mary introduces magical elements always leaves it open to a different interpretation, where there maybe is no magic and the children simply believe it was because of their imagination.
- Maybe the children did physically clean up their toys, but Mary distracting them by turning it into a game, so the children didn't even realize they were doing a chore. When they finish their game, they realize their room is cleaned "without any effort".
- Maybe Uncle Albert was just really good at making the children laugh, and they laughed so much until they were light in the head.
- Maybe Bert simply showed them amazing drawings of the horseraces, penguin restaurant, etc. He may just be a really good storyteller (which seems to be the case based on his interactions with the children), and he is able to make the story come to life. The actual animation we see in the movie may simply be the imagination of the children based on the stories and songs Bert tells/sings them; while in reality they're still standing in the park next to the drawings, dancing with Bert.
That's the thing about children: the line between imagination and reality is rather blurry. Since the movie is from the children's perspective, this means the viewer may simply be drawn into the children's imaginary world.
But I think this is a cover story. It seems Mary Poppins truly has magical qualities (it's not just imagination). There's no real explanation for her flying umbrella, the children didn't even know her when she landed; so they'd have no reason to make it up at that point in time.
Assuming she is indeed magical, she seems to still intentionally approach it in a way that the adults never find out about it, and she always has a more realistic explanation for what they did (much like my bullet point examples above).
She barely needs to actively work at hiding the magic, as shown by Mr Banks' immediate assumption that the children are embellishing their story about the adventure in the park. Mr Banks, just like most adults in a kids' movie, has no vivid imagination anymore and is more likely to assume the children are embellishing rather than speaking the truth about their magical nanny.