This worked out ok for me in the end - I think it's possible to "reserve" a ticket on JAL without paying initially, and the email notification includes the slightly ambiguous text to mean that if you don't pay by the specified date you'll lose the reservation.

In my case - as seems to be the same with yours - by paying as I booked online there was no need to make any further contact with JAL or adjust anything on the website etc, and my booking was all in order when we arrived at the airport. Annoyingly the four digit reservation code (rather than the six digit international codes) isn't checkable on any other system like checkmytrip etc, but it is the correct format when you show up at the airport.

Hope this is reassuring!