Welcome to the Wefugees Community and thank you for reaching out to us.
You did right in submitting a so-called "Umverteilungsantrag" (request to live in another city/municipality within Germany) to the immigration office ("Ausländerbehörde") - that is the only way to get a permission to move to another place during the pending asylum procedure. I am a bit surprised though, that the Ausländerbehörde asked already for a rental contract before they decided on your Umverteilungsantrag. I am afraid that you need to cancel the contract again in case the Umverteilungsantrag gets denied. Please note that you can also appeal (Widerspruch einlegen) against a potential negative decision. Unfortunately, the Bundesagentur für Arbeit is not involved in any residence aspects - they only check the conditions of the work/the job offer itself.
I would highly recommend you to contact a migration counselling office as well in case your application gets denied. Please let us know if you need support in finding a respective office in your area.
Would you agree on my explanations and is there anything you would like to add, dear @mbeon-fardeen?
I hope this helps and don't hesitate to get back to us with any further questions.
All the best,