N.,
I can SO relate! When my daughter was 2.5 she had an automatic toilet flush under her unexpectedly, twice in a row. On both times she got her bottom splashed which was an insult to boot. Since then she has been afraid to go on "those toilets". She is now 6.5!
At first I tried telling her that it wouldn't happen again but of course, it did. Then, I'd hold my hand in front of the sensor. I also bought a pack of colorful PostIts to put over the sensor but that was a temporary fix. Finally, what I did, was take a survey of the toilets in the businesses I frequented and the ones that did NOT have automatic flush toilets were the ones that I shopped at. I have also gone to the extreme of making mental maps of which bathrooms, restaurants and welcoming stations between here and the grandparents' houses have these dreaded toilets. Just telling her that she's going to have to sit on one causes her to go into a panic and she will literally pee on herself instead of sit on one.
Businesses have gone to automatic toilets because people are lazy and don't flush. Then others poop right on top of the mess the others left behind and also don't flush. Pretty soon you've got an overflowing toilet and that's not only a messy health hazard, it's expensive to fix. Also, it costs less money to have the toilets essentially clean themselves (by flushing every time) than to hire cleaning crews or have the employees check them ever so often.
K.