Whether or not you call it an addendum, yes you need a signed agreement for all terms of this agreement.
I would lay out in it the actual specs of the work to be done, the contractor who will perform the work, the estimated cost and the fact the tenant will deposit funds with the LL BEFORE the work begins for their share. Also put in there the fact that they have requested this upgrade, offered to pay half and agree to the following:
AT NO TIME either DURING the tenancy or when it ends regardless of when that is will the tenant receive "credit" for having paid for 1/2 of this upgrade. Be sure to format this agreement in standard legal format...define the parties, use the correct terms, etc.
ALSO, be sure to put in there the obvious, that this is a "permanent" alteration to the property and will remain fully intact with the property regardless of if/when their tenancy ends, etc.
But YES you do need a signed agreement that should reference their rental agreement, etc.
--207.200.xxx.xx