The RASCI being developed is intended to highlight the support model going forward. From my perspective a RASCI encompasses all aspects of the project including handover.
It can do both, or neither. RASCI is just a tool to get agreement and understanding on who is responsible for what and at what level.
If it's useful to have as part of your project (lots of deliverables, lots of stakeholders, lots of "opinions" etc) then by all means use it for the entire project.
If it's useful only in certain phases of the project (eg handover and/or operations) then use it only in those phases.
Neither is fundamentally right or wrong, RASCI is just a tool that becomes part of your kit. I find it very useful in larger teams or complicated (or overly bureaucratic) organisational environments to use over the entire project process, but for smaller projects / closer knit teams / collaborative organisational cultures I sometimes find it overkill and use it only for certain phases, and sometimes not at all.