a visa, a multiple entry visa, an extension, and a re-entry permit are different things. Anytime you wish to leave the country you either have to ensure that you have a multiple entry visa or if you have a single entry visa you'll need to buy a reentry permit to keep that visa alive. extensions do not come with reentry permits so once you get an extension then you immediately buy a reentry permit either single or multiple if you plan to leave the country and return and keep your extension alive.
Where was this person entering from, all they can really do is send them back to where they came from, can they force them to go back to America if they didn't arrive from America?
Some offices won't issue one until after your first 90 day report, and of course you need to have a TM30 filed in their jurisdiction for them to supply the certificate.
Look at the Jakarta embassy website and look at their processing times. I'd have the course date start a month to 6 weeks from your visa application date. Do you buy a visa to Bali? Regardless, you'll have boarding passes and hotel reservations. They'll want proof you're there, get creative, don't go through the electronic gates.