It often takes a while for the probes to stablise and get an accurate reading, so this is a very common pattern, but I haven't looked into why. I think part of it may be the machine calibrating to the flow of blood through the area of skin you have chosen. You often apply the probe and sit it there for 30-60s waiting for it to stabilise.
If you are worried, ask them to leave it on throughout your consult. You should see it sit at 99-100% for the rest of your stay.
That single person you are paying a sub-par wage won't be providing 24/7/365 support, which is a big benefit of AWS / cloud providers. It's also a bit of insurance on your hardware in case of failures, free replacement. Finally, if something catastrophic was to happen, with a recent-ish offsite backup it's usually pretty trivial to setup on a different region or even cloud provider. With your own hardware, that's a bit harder.
I agree though with one of the parents, AWS costs here can likely be significantly reduced. I cut costs in half by (a) reserving instances and (b) thinking about EBS and downgrading / downsizing where possible rather than using the defaults.
If you are worried, ask them to leave it on throughout your consult. You should see it sit at 99-100% for the rest of your stay.