Is this 1800 calories including working out, or 1800 calories after subtracting the ones you've burnt?
That's dependent on the app. Some "smarter" apps might incorporate your activity. Most just ask if you're "high active", "moderately active", "little bit active", etc. Some really ignorant apps will just take your age, weight, and height and guess.
Is this why programs such a slimming world who don't actively incorporate calories into their plans are so successful?
I don't know enough about this plan to say. They are most likely incorporating calories in the equation whether they tell you or not. For example, Weight Watchers uses a points system which is really just a very simple way to count calories.
But yes, if they limit your food intake then encourage exercise, then you will lose weight over time if you adhere to it. Weight loss programs also will over-exaggerate their numbers because they know people won't follow it fully. They just cater to people who are not in the habit of living a certain lifestyle, old habits die hard, and they incorporate it in their programs so they work in general.
Also are there any repercussions of eating significantly under 1800
for example 1200kcals as well as doing exercise (other than feeling
You'll lose a significant portion of lean mass which will slow your metabolism down. This makes it harder to keep the weight off in the long term.
An extreme example, there is a show in the U.S. called the Biggest Loser (not sure if it's in other countries). In that show, they take really obese people and torture them for months by putting them on extremely low calories while forcing them to do high intensity exercise. There are studies now that show that their metabolism is wrecked. Almost all the contestants regain their weight. The ones that kept it off are struggling all the time.
So in the world in fitness and weight loss, slow-and-steady wins the race. If you lose more than 2 lbs. or 1 kg. a week, then you need to raise those calories. Typically 0.5 lbs. / 0.25 kg. to 1 lb. / 0.5 kg is the sweet spot.