Rental Lease Agreement - when does it start?

[Raj Kumar]

I have a unit I am trying to lease. This unit lease start date is in November and I have interested parties who are interested in renting it in November. I am deciding to finalize one of them  and are using the standard verbiage for the Lease (inlcuding Lease termination - 60 days notice - X times rent early termination fee etc). 

My question was - it is TWO months since the tenants will officially take over the lease. What if they decide after 1 month they dont want this lease and ask to back out? Am i protected by the potential loss of rent due to finding new tenants, spending the time again etc by making them aware that the Lease termination starts as soon as they transfer the Security Deposit and 1st months rent (I will consider this minimum as soon as they sign the lease) but i am concerned about if they ask something like "Please give us our security deposit etc back - we found another place" AFTER signing the Lease but before the Lease actually starts?

This is in NJ FYI.