View PDF After Exporting is available from the General panel of all the PDF presets.
It's a sticky feature which will remain in effect after you set it. It's not saved with a PDF preset.
Because it's a sticky feature, it will apply with any PDF preset. Basically, if you set it, you don't need to worry about it, unless you have another person using your copy of InDesign.
And it will open using the default PDF reader.
So, to clarify, as Bob says, it will open in whatever PDF reader your operating system is set up to open PDF files. If you need to change it, you change it in the OS, not in InDesign.
Thanks, everyone, for your answers.