Improve temurin special case is not handled on the caller side ?

@sxa, @karianna Why this special case is not handled on the caller side ?
temurin is not a JVM so the JVM arg must not accept "temurin" and hide some other value behind ..

If you set upsteam a vendor name temurin , his place is in VENDOR_BRANDING from this script, not in JVM arg

I think in caller job you must do somthing like that:
if (VARIANT == "temurin" )
VENDOR_BRANDING"=Temurin"
JVM="hotspot" // default JVM for VARIANT "temurin"
call createInstallerJob
fi

_Originally posted by @douph1 in https://github.com/adoptium/installer/pull/438#discussion_r810872958_

Start by locating the caller job that invokes createInstallerJob and inspect how VARIANT, JVM, and VENDOR_BRANDING are passed. Confirm how the temurin variant is represented, then verify that its vendor branding and default JVM value are handled before the installer job is created.

Written by the indexing model from the issue text.