I still consider this a serious bug in the donwload custom control .
Meanwhile I have developed a workaround by showing the attachments in a dataTable with correct links, working as expected in the Notes client and in the browser:
<!-- Attachments in body field of dominoDoc with correct links... -->
<xp:dataTable id="dataTable1" caption="Attachments" var="attRow">
<xp:this.value><![CDATA[#{javascript:dominoDoc.getAttachmentList("Body").toArray()}]]></xp:this.value>
<xp:this.rendered><![CDATA[#{javascript:getComponent("dataTable1").getRowCount() > 0 }]]></xp:this.rendered>
<xp:column id="column1">
<xp:link escape="true" id="link2" target="_blank">
<xp:this.value><![CDATA[#{javascript:
// each attRow is a NotesEmbeddedObject
var attName = attRow.getName();
var domDocServerPath = dominoDoc.getParentDatabase().getServer();
var domDocDbPath = dominoDoc.getParentDatabase().getFilePath();
domDocDbPath = domDocDbPath.replace(/\\/g,"/");
var domDocUnid = dominoDoc.getDocument().getUniversalID();
var res = @Word(context.getUrl(),'.nsf',1) + ".nsf/xsp/.ibmmodres/domino/OpenAttachment/" + domDocServerPath+"!!"+domDocDbPath + "/" + domDocUnid + "/body/" + attName + "?Open";
res}]]></xp:this.value>
<xp:this.text><![CDATA[#{javascript:attRow.getName()}]]></xp:this.text>
<xp:image id="image2" url="/intprof.gif"></xp:image>
</xp:link>
</xp:column>
</xp:dataTable>