Then there must be some buffering issue. It's the same Java used by both browsers, so it must be a different program executed. I assume still the "old" version is running in Firefox.
To make sure:
(1a) Clear your Firefix cache (somewhere in "Einstellung > erweitert")
(1b) Close Firefox
(1c) Make sure that really all Firefoxes have disappeared from Task Manager
and
(2) open "Systemsteuerung > Java > Temporär Internetdateien > Anzeigen..." and remove all from the list.
(1b), (1c) and (2) should not be necessary, so you may try step by step in order to see which step solves the problem.