I have the 32 and 64 bit versions of Processing installed and export from these to have both versions.
It does clearly state what target platform you are exporting to in the window.
I have not done this in a while but did come across this issue at one time.
I did find this:
https://processing.org/reference/environment/#Export
Following the links it states:
We strongly recommended that you embed Java with your application. Not including it opens a pandora’s box of problems that can happen when people try to run your project.
:)