I've done it too. For a long time.
Basically, what they've told you is right. The way it works is that the person being cared for has their needs assessed and an allotted time is given that the assessor deems is necessary to carry out the tasks required. As long as the tasks are completed to the required standard, the carer is not obliged to stay - and they will have been told this is the way it works by their employers.
Also, the points made by others are valid. The system is screwed. They're not paid for travelling time, but worse than that travelling time isn't even allowed for! So your rota will look like this . . .
7.00 Mrs X (15 minutes)
7.15 Mrs Y
Never mind the fact that it takes 10 minutes to get from Mrs X to Mrs Y's house! As they'll usually have around 6 calls to make that morning, the travelling time thing has a serious knock on effect!
Equally if Mrs X is only allotted 15 minutes, but the carer arrives to find she's in a situation where she needs longer than that, the carer would be expected to stay longer in order to carry out proper care and just put in a call to their manager, who SHOULD really then cover some of their other calls to compensate, but who probably won't and will probably tell them not to worry about it and just carry on - not terribly helpful as it's the carer feeling the pressure on the front line getting shouted out by Mrs Y for being late.
However, having said all this, you do get some shit carers who will run in and out without carrying out proper care - so you need to watch for that.