LiveConnect : Some roundtrip scenarios does not work on FF/mozilla while works fine on IE

Build Tried : Promoted 6u2 JRE build
OS : Windows XP
Problem:
Below listed scenarios works fine on IE but they are not working at all on mozilla and firefox.
- bug is also reproducible with 1.4.2_15 and 1.5.0_12
Scenario I :
- Try loading the following URL inside IE or firefox/mozilla browser
http://sqeweb.sfbay.sun.com/deployment2/jitu/deployment_mustang_UR_int_ws/deployment/src/plugin/LiveConnect/LiveConnect/html/Roundtrip1.html
- Link to Java sources
http://sqeweb.sfbay.sun.com/deployment2/jitu/deployment_mustang_UR_int_ws/deployment/src/plugin/LiveConnect/LiveConnect/src/TestApplet.java

On IE :
1) Pop-up "enter JavaScript" should be there.
2) Second Pop-up "re-enter JavaScript" should be there.
3) "Round Trip Test completed successfully" should get displayed inside the browser.

On Firefox/mozilla :
1) Pop-up "enter JavaScript" should be there.
2) Second Pop-up "re-enter JavaScript" is not coming up, it means javascript method "reenterJavascript(s)" is not getting called from an applet.
3) As a result "Round Trip Test completed successfully" is not getting displayed inside the browser.
#2 and #3 should be same as of IE.
If you notice the above mentioned behavior then bug is reproduced.

Scenario II :
- Try loading the following URL inside IE or firefox/mozilla browser
http://sqeweb.sfbay.sun.com/deployment2/jitu/deployment_mustang_UR_int_ws/deployment/src/plugin/LiveConnect/LiveConnect/html/RoundTripDiffApplets.html

Link to Java source:
http://sqeweb.sfbay.sun.com/deployment2/jitu/deployment_mustang_UR_int_ws/deployment/src/plugin/LiveConnect/LiveConnect/src/Applet1.java
http://sqeweb.sfbay.sun.com/deployment2/jitu/deployment_mustang_UR_int_ws/deployment/src/plugin/LiveConnect/LiveConnect/src/Applet2.java

On IE :
- Pop-up "_test() called" should be there.
- Second Pop-up "_test2() called" should be there.

On Firefox/mozilla : No pop-up is coming but in actual behavior should be same as of IE
If you notice the above mentioned behavior then bug is reproduced.