Based on the description of the NOW() and TODAY() functions, I would guess that your Tableau Online site is hosted on an instance where the system time is in UTC. Those two functions will use the system time from the operating system that is hosting Tableau Online, there is more detail about which servers are in which timezones at the bottom of this article: Data Update Time Displaying Incorrect Timezone When Published
The workaround for this behavior would be to use a calculated field to convert NOW and TODAY into the relevant time zone.
Yes my Tableau online server is hosted on a UTC operating environment.
I have actually played around with using calculated fields to offset the time between EST and UTC but because you need to specify the actual number of hours to offset and not reference a time zone during time of day light savings all my data is going to be thrown out by an hour so it's not really a workable approach.
Thank you for taking the time to reply.