The journey of kata should be to first develop all the right technical aspects, making sure you dot all the I’s and cross all the T’s.
There is no point being fast or explosive if you have poor technical habits as these will not serve you well in self-defence. Liken it to putting a lousy driver behind the wheel of the best Formula 1 car; they are not going to win the race. Too often students aim to impress with their speed, focus and effort. The problem is their instructor wants to be impressed by seeing they have a handle on driving the kata first and can successfully negotiate the course.
The best way to achieve this is to practise at home (you might also practise before and after class). When you practise, go through the kata in super slow motion. Going through in super slow motion enables you to really think about each and every aspect of each movement. This allows you to perform it correctly, creating muscle memory and positive habits. It also allows you to identify poor habits (and correct them), habits that you may not have identified at regular pace.
Once you have practised it a few times in super slow motion, build it up to medium pace and then finally at regular pace.