Do cats follow their owners? I depends. Some cats will follow their owners and some are less inclined to do it. It depends on the individual cat and the circumstance.
Some will say that when cats follow their owners around it is a sign that they love their owner. Others will say it is more likely to be attention seeking. My cat follows me a lot as I am at home a lot in retirement. It is described as dog-like behaviour but it isn’t. It is normal for cats to do this and it helps to create a very close relationship.
My cat’s world revolves around me (and vice versa to a certain extent). It is bound to. He likes to be near me; touching me and being friendly to me. I reciprocate. This is not my cat loving me in the human meaning of the word or seeking attention but being friendly and enjoying the relationship with his human companion.
Domestic cats like to be in contact with cats and humans (surrogate cat) with whom they are friendly.
The answer to the question: do cats follow their owners, is that they are likely to, on occasion, in a household where the human is around a lot of the time. But it depends on the character of the cat and the human. An extremely warm cat owner can bring unexpectedly friendly behavior out of a cat.
There is a recent story about Jake Perry who has an unusual way of looking after domestic cats. He creates a superbly friendly environment because he loves his cats deeply. I am sure that some of them follow him around.
There are specific circumstances when cats will almost certainly follow their owner around; for instance at meal time. If a routine has been set up like going to a patio door to go out into the garden, an activity that the cat is particularly fond of, he or she will follow his owner to the door every time. It’s informal training for both human and cat.
Do cats follow their owners? Yes, often but not always.