Your porting request is submitted to the donar network (eg., Airtel, Vodafone, Idea etc) by Reliance Jio immediately after you submit your fingerprints and Aadhar Card. You must get an SMS with-in 24 hours saying "Your porting request has been approved". If everything goes smooth with MNP, you should be able to start using your new SIM card with-in a week.
You will be notified over SMS 24 hours before your network would switch to the new telecom network. They will specify before hand (in the SMS), the exact time at which the switch will happen. At this time, you should see that your current SIM will no longer work - that means its time you replace your old SIM with JIO SIM.
However, the donar operators are playing cheap tricks in order to reject your porting request. They are trying their best to reject your porting request. So, my caution to the post-paid users of Vodafone and Airtel to clear all your bills and pay excess amount on top of unbilled amount, so that you will not have to have any outstanding balance to your old operator. Do this before your request your porting.