Few people here, if any, use the pen as it was designed. The pen only doses in whole units and there has been discussions in the past about the pen not dosing exactly a whole unit either and fur shots. The Human instructions are to poke the needle into the skin, hold the button, wait until the 0 appears in the window, then remove the needle from the skin. The instructions would work the same for a cat.
Is there a reason why you aren't using insulin syringes with the pen? If the vet told you to use the pen the way Human diabetics use it, you can safely ignore the vet. Many vets are not familiar with using insulin pens for cats. By using syringes, you can easily dose half unit and even quarter unit doses which cats do need sometimes. You want U100 3/10 cc syringes with half unit markings. Your vet can write you a prescription to buy from any Human pharmacy or you can look online to buy syringes. Amazon is one place that does not ask for a prescription. Some online places will ask for a prescription or the vet's phone number depending on what state you live in. If you're not in the US, other members may suggest where to buy syringes from.