I took a look at the time zone property on my registration module via the Site Settings > Profile Properties section, and the preferred time zone property was set to a type of 'TimeZoneInfo'. I changed the property type 'TimeZone', and now new user registrations do show the correct time zone.
However, when I changed this type property, all of the old users no longer have their preferred time zone recognized correctly by the Users module.
The TimeZone type property (the one that I updated to) has drop down options with code that looks like this:
<option value="-480">(UTC -08:00) Pacific Time (US & Canada); Tijuanaoption>
So in my database I now have values like '-480' stored in the tables. While the Users module is able to recognize this format when I changed the type, all of the users who registered when I had prior versions of DNN installed have values stored in the database with the format of something like 'Alaskan Standard Time', which is apparently no longer recognized by the Users module when I changed the timezone property.
So now it looks like the Users module is looking for a value that is aligned with the type value I have selected for the preferred time zone, but it's not backwards compatible to recognize both formats?