Gardeners or mobile hairdressers or personal trainers (for completely random examples) don’t charge you for travel time, like in my pp it’s only when there’s animal care involved that people get really weird about how much you should be paying
Any self-employed service rate needs to take into account non-billable hours (admin, marketing, travel time, accounts, providing quotes, handling enquiries, etc.) and the lack of employment benefits (guaranteed hours, employment protection, sick pay, holiday pay, pension contributions, redundancy, etc.) to be viable and sustainable.
My window cleaner charges £16 for 15 mins cleaning my windows. Of course (!!!) he will have sat down and taken into account travel time and how much he needs to charge to make the rate enough to cover his time between jobs. He’d be an idiot not to.
((He also works a round, obviously organising his route with the least possible journey time between jobs. Obviously you need to build up quite a large customer base to do this, and have a big enough market. Windows can be cleaned at any time of the day, whereas I’d expect most pets want feeding morning and evening.))
Same for gardeners and personal trainers and anyone else who works one hour at a time at separate locations.
It might not be of interest to you, but if their travel time is 10 minutes there and 10 mins back to your home for a half hour visit, they are spending 50 minutes on your job.
Of course they need to take this into account when charging. (Along with all the other factors mentioned above.)
In the case of the OP’s sitter, she should have a conversation with her, because obviously their expectations are misaligned. Is it that the visits are set by default in 30-min slots (i.e. there’s not an option to set a 10-min visit via the platform even if that’s all that’s needed)? Is it that the slot has allowed for up to half an hour (if needed) to do the agreed tasks?
OP, if you want her to spend longer, just ask if she would sit with your cat for 20 mins after she’s fed her. I should think she will be happy to do so, and obviously if not then just find someone else who can.