I have used dp:variable extensions in XSLT in the past.
Your syntax looks good to me.
Have you included xmlns:dp="
http://www.datapower.com/extensions" in your XSL?
Try this :
<?xml version="1.0"?>
<xsl:stylesheet version="1.0" xmlns:xsl="
http://www.w3.org/1999/XSL/Transform" xmlns:soap="
http://schemas.xmlsoap.org/soap/envelope/" xmlns:tns="
http://www.example.org/tns" xmlns:dp="
http://www.datapower.com/extensions" extension-element-prefixes="dp" exclude-result-prefixes="dp">
<xsl:output method="xml"/>
<xsl:template match="/">
<someRootElement>
<responseheader:DestinationSystem>
<xsl:value-of select="dp:variable('var://context/tempvar1/request/OriginationSystem')"/>
</responseheader:DestinationSystem>
<responseheader:OriginationSystem>
<xsl:value-of select="dp:variable('var://context/tempvar1/request/DestinationSystem')"/>
</responseheader:OriginationSystem>
<responseheader:CorrelationID>
<xsl:value-of select="dp:variable('var://context/tempvar1/request/MessageID')"/>
</responseheader:CorrelationID>
</someRootElement>
</xsl:template>
</xsl:stylesheet>
(I haven't had a chance to test this yet)