Based on @sjohnson's answer, @sk4l's comments, and some research of my own, I've sort of figured out what's going on in my environment:
The setting indexed_realtime_use_by_default in limits.conf was true .
In addition, there is another property indexed_realtime_disk_sync_delay which was not set, which means that it was using the default delay of 60 seconds (which is why I saw the 60 second delay I mentioned in the original post).
The delay time mentioned above is the amount of delay for indexed real-time searches (to make sure the data gets fully processed and indexed and synced to disk). That means that I could still do non-indexed real-time searches with no delays. However, for an indexed search, there will be the delay. It's been pointed out to me that there's a significant performance hit for performing non-indexed real-time searches though, so there's a trade-off there between the performance hit and the delay.
My use case was to see data over the past couple of seconds as it comes in, so doing a non-indexed search could be an acceptable solution in my case.
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