And it does. Copying any app bundle to an indexed disk, like your boot drive, will cause it to get indexed immediately.

There are the occasional bugs though, and there’s also aggressive caching.

If more non-store Mac apps had an "Install" process, you would.

But you're just dragging a special type of folder off a disk image, so nah.

This was a weird coincidence or bug, nothing more. I've used free and trial versions of IntelliJ on Macs countless times without search ever having issues with them. It's hard to imagine how you'd even make the system work in that way, as an app developer.