You are correct. With the exception of a few specific paging-only channels, all Part 90 frequencies between 150-470 MHz were required to be narrowband starting 1/1/2013. It's likely the entries you are seeing in the RadioReference database have simply not been updated yet. That said, there is a possibility the agencies were issued a waiver to extend the deadline, or failed to take any action at all. Try programming those channels as narrowband first, and if they are much louder than other channels, or sound distorted and/or clipped, reprogram them as wide.
As for NXDN, there is a slight difference in the sound of the raw data stream between 12.5 kHz (narrow) and 6.25 kHz (very narrow) NXDN. 12.5 kHz NXDN has a much more noticeable "pattern" in the data stream, whereas 6.25 kHz sounds more like open squelch. Here's a link to a recording
where the difference is demonstrated. You can also tell which mode an entity is licensed for by looking at the emission designators on their license: 4K00F1x is 6.25 kHz, and 8K30F1x is 12.5 kHz NXDN. You may find that they are licensed for both, however.