If the iOS app is active (either on screen or in the background) while the day transitions to the next, the 'today/current day' indicator will remain on the original date (the one on which the app was initially opened on). In order to switch the indicator to the next day, the app needs to be force closed and reopened (or it needs to 'expire' in the background on its own, if the iOS memory manager closes the app eventually).

See the screenshot attached below for a reference of said 'today/current day' indicator (the gray circle). Note that the screenshot is an example and is not showing the bug with today's date (but this is what it would look like if the app were active on Wednesday night, after transitioning into Thursday).