They do slip and slide, to get the best times you need to find the point just around where they start sliding, too much and you lose time and can overheat the tyres.
There's also the tyre model which is a kinda odd/broken at the moment, it has many good factors but also the main major flaw is the temperature modelling, the heat build-up is somewhere near right but the grip levels are better when cold, so the first lap will feel great and then it will start slipping more during laps 2/3 but then settle down once the top temps are reached.
It is just practice though, I've not driven the MX-5 (assuming you're doing road stuffs) in a long time and over various iterations of the tyre model so probably can't help much, but ultimately keep doing laps, aim first for consistency and then for speed, but just learn the car/tyres/feedback.
With they tyres, there is a new software build tomorrow, which does include a couple of things with the tyres which may or may not have a big effect.