Here is how I do it for 2 jobs with 3 parameters each. Strange that the "snippet generator" does not work, at least it does for me on jenkins 1.620. Are you sure you point to the correct parametised job ?
String outputDirTimestamp = new SimpleDateFormat("yyyy-MM-dd-HH-mm-ss").format(new Date());
// "env.mySoftVersion" has previously been set in env
// "packagingGitBranch" is set elsewhere
parallel(win: {
build job: 'packaging_win', parameters: [[$class: 'StringParameterValue', name: 'outputDirTimestamp', value: outputDirTimestamp], [$class: 'StringParameterValue', name: 'branchToPackage', value: packagingGitBranch], [$class: 'StringParameterValue', name: 'mySoft.version', value: env.mySoftVersion]]
}, lin: {
build job: 'packaging_linux', parameters: [[$class: 'StringParameterValue', name: 'outputDirTimestamp', value: outputDirTimestamp], [$class: 'StringParameterValue', name: 'branchToPackage', value: packagingGitBranch], [$class: 'StringParameterValue', name: 'mySoft.version', value: env.mySoftVersion]]
})