WA Security Deposit return before lease end date?

[Kevin S.]

Hi!

I have a tenant that recently moved out of a single family residence in WA state.

- Lease end date was April 25

- Lease required 60 day notice, they gave notice on March 20, but opted to pay rent through May 31 to allow flexibility for their move.

- Signed a lease termination agreement ending the lease on May 31

- Tenant moved out on April 10

- A new lease was signed on April 28, final rent due was prorated to allow new tenants to move in May 22.  

Does the tenant need to make the final rent payment?  If it is not paid, can late fees be assessed?  When does the security deposit need to be returned?  
My thinking here is the security deposit is not meant to be used to pay that last month of rent.  Additionally, if the payment is not made, late fees will apply.  I am also under the impression the deposit does not need to be returned until 21 days after the lease termination date (not the move out date).

https://apps.leg.wa.gov/RCW/de...

Thoughts?  I want to make sure I'm doing this right. Thank you so much in advance.  I'm a long time BP lurker and podcast listener.  Awesome community!