Help understanding lease terms

[Cliff T.]

Hi all,

I'm hoping I can get some clarity with a lease that I've signed with my tenants. Their lease technically ends on Sep 30, 2018 and I was given verbal notice today that they will be leaving when their lease ends. The tenants are adamant that they are allowed to leave on Sep 30, while I believe their move-out should be on Oct 31, after factoring the 30-day notice which requires them to pay rent for the following month since we're already one week into September.

Here are the salient clauses in the contract that we signed. Based on the below, when are my tenants allowed to move out if they gave notice today?

Clause 1 TERMS: Resident agrees to pay in advance $XXX per month on the 1st day of each month. This agreement shall commence on Sep 1, 2017 and continue until Sep 30, 2018 as a leasehold. Thereafter it shall become a month-to-month tenancy. If Resident should move from the premises prior to the expiration of this time period, he shall be liable for all rent due until such time that the apartment is occupied by an Owner approved paying Resident and/or expiration of said time period, whichever period is shorter. 

Clause 17 TERMINATION: After expiration of the leasing period, this agreement is automatically renewed from month-to-month, but may be terminated by either party. The owner giving 60 day notice and the resident giving a 30-day written notice of intention to terminate. Where laws require "just cause" such just cause shall be so stated on said notice. 

Thanks in advance,

Cliff