Unopened Mayo does not need refrigeration and can sit out at room temperature.
However once you open a jar of mayo then you need to refrigerate the mayo to keep bacteria from growing in it as mayo does contain ingredients that can spoil once the jar of mayo is open.
But it's okay if you happened to leave the jar of mayo out overnight with the lid on the jar of mayo.
But really mayo should be refrigerated once opened to keep it from spoiling.
But Ketchup even when opened does not need refrigerated.
Ketchup can sit out all night.
Ketchup does not need refrigeration and you can leave Ketchup out at room temperature until you use it all up.
Whether opened or unopened the bottles of Ketchup can sit out all night and for months before it goes bad.
I never refrigerate any Ketchup I have and some bottles of Ketchup I've kept out at room temperature for 6 months before I used it all.
You can refrigerate the Ketchup but there's no need to refrigerate the Ketchup as there's nothing in the Ketchup that will spoil and make you sick.
Ketchup and even Mustard can be left out at room temperature without requiring refrigeration.
Only refrigerate the Ketchup and Mustard if you want too but there's no requirement to do so.
Ketchup actually lasts longer when left out at room temperature.