I can't exactly reproduce this bug in version 1.5.6.
Here is what I get:
Given a class A and a class B, I draw a composition between A and B
----         ------
| A | <>-----|  B  |
-----        ------- 
The generated javascript code is
File A.js:
----------------------------------
**
  * class A
  */

A = function ()
{
  this._init ();
}


/**
 * _init sets all A attributes to their default value. Make sure to call this
 * method within your class constructor
 */
A.prototype._init = function ()
{

  /**Aggregations: */

  /**Compositions: */
  this.m_A = new A ();

}
-----------------------

File B.js:

-----------------------
**
  * class A
  */

A = function ()
{
  this._init ();
}


/**
 * _init sets all A attributes to their default value. Make sure to call this
 * method within your class constructor
 */
A.prototype._init = function ()
{

  /**Aggregations: */

  /**Compositions: */
  this.m_A = new A ();

}
--------------------------------

According to me, there are two errors:
1) There shouldn't be a composant m_A in class B but a composant m_B in class A (In this case, the C++ generated code doesn't generate any composants in any classes. The C++ generated code generates a composant m_B if only I add a attribute of class B in class A)
2) There shouldn't be a composant m_A in class A. In my example, there is only one composant m_A in class A. That's better than many  but still incorrect

PS : The generated code is identical in trunk

SVN commit 634263 by okellogg:

writeClass (aggregations, compositions): Do not generate code when `c´ is at role B.
 Generate code for the role B object.
BUG:135527


 M  +1 -0      ChangeLog  
 M  +10 -4     umbrello/codegenerators/jswriter.cpp  


--- branches/KDE/3.5/kdesdk/umbrello/ChangeLog #634262:634263
@@ -3,6 +3,7 @@
 * Bugs fixed from http://bugs.kde.org:
 * %date% and %time% not being parsed (96612)
 * Relationships for entities do not live outside of an entity relationship diagram (125146)
+* Javascript wrong Code Generation (135527)
 * Javascript Code Generation creates bad format methods (135540)
 * Crash when deleting the link between a package and a class (141602)
 * Ada95 Code Generation Errors for Aggregation (141644)
--- branches/KDE/3.5/kdesdk/umbrello/umbrello/codegenerators/jswriter.cpp #634262:634263
@@ -155,8 +155,11 @@
         js << m_endl << m_indentation << "/**Aggregations: */" << m_endl;
         for (UMLAssociation* a = aggregations.first(); a; a = aggregations.next())
         {
-            QString nm(cleanName(a->getObject(Uml::A)->getName()));
-            if (a->getMulti(Uml::A).isEmpty())
+            UMLObject *b = a->getObject(Uml::B);
+            if (b == c)
+                continue;   // we need to be at the "A" side and the other guy at "B"
+            QString nm(cleanName(b->getName()));
+            if (a->getMulti(Uml::B).isEmpty())
                 js << m_indentation << "this.m_" << nm << " = new " << nm << " ();" << m_endl;
             else
                 js << m_indentation << "this.m_" << nm.lower() << " = new Array ();" << m_endl;
@@ -168,8 +171,11 @@
         js << m_endl << m_indentation << "/**Compositions: */" << m_endl;
         for (UMLAssociation *a = compositions.first(); a; a = compositions.next())
         {
-            QString nm(cleanName(a->getObject(Uml::A)->getName()));
-            if(a->getMulti(Uml::A).isEmpty())
+            UMLObject *b = a->getObject(Uml::B);
+            if (b == c)
+                continue;   // we need to be at the "A" side and the other guy at "B"
+            QString nm(cleanName(b->getName()));
+            if (a->getMulti(Uml::B).isEmpty())
                 js << m_indentation << "this.m_" << nm << " = new "<< nm << " ();" << m_endl;
             else
                 js << m_indentation << "this.m_" << nm.lower() << " = new Array ();" << m_endl;