I just had the same problem. I am playing on th PC, but with a controller. I only saw the announcement how much time was left until the start of the next month, but not the rewards for the current month. There was no option to claim a reward while using the controller interface.
When I switched to the standard keyboard interface, I still did not see the current reward list. But there was the option shown to claim todays (invisible) reward with the standard keyboard setting "E", which worked.
So switching the interface might be working for otherrs too.
This happened to me as well. I was playing last night, got the notification, went to claim it, and it, and could not. I checked again this morning, the notification is still there, yet the calendar screen boxes are empty, and the headline is the new month begins countdown.

Found this on the support page:-
https://help.elderscrollsonline.com/app/answers/detail/a_id/43864/p/1
Seems a bit hit-and-miss for me, but worth a go.