What version of adTempus?
I am assuming that the jobs involved are all on the same computer--there's a bug that causes adTempus to say the condition is on a remote computer even if it isn't. If that's not the case, let me know.
I also assume that deploying the setup to the production environment involved exporting the jobs from the development server to the production server.
If so, the links between the jobs will be broken unless you exported the target (upstream) jobs along with the dependent jobs (or the target jobs had been previously exported from dev to prod). This is because the condition doesn't link based on the job's name but on the Job ID (which you can see under the name in the job properties window).
In your case I imagine something like this: in your dev environment you have Job B with a condition on Job A. Job A has a Job ID of "{62391774-557D-426D-932A-EA58D647317B}".
In your production environment you have a "Job A", but it was created directly on that computer (not originally exported from the dev computer), so it has a different Job ID.
You exported Job B from dev to production, but not Job A. When Job B runs, it doesn't look for "Job A"; it looks for the job with Job ID "{62391774-557D-426D-932A-EA58D647317B}", which doesn't exist on the new server.
You should be able to fix this by editing the Condition once the job gets to the prod server and re-selecting the target job. This will recreate the link using the correct Job ID.
If you exported both the target and dependent jobs from dev to prod, then something else is going on, because the link should have been adjusted during the import in that case.