I post here an experience from an expat who renew the visa and is been told by the police that's going to change.
I copy and paste the following message:
Please spread the word to everyone entering Jordan with a new Visa. I got this info today from my local police station:
As of October 1st, you must report to your local police station within the first 14 days of entering Jordan and bring the same documents you would need if you were extending your visa after the first month (passport, passport copy, copy of rental agreement, copy of landlord ID). They want your address within the first 14 days. Anyone late will face a fine of 200 JD.