No, the OCI does not need to be reissued. When passport #2 expires and a new passport (#3 ) is obtained, then it will be required to have the OCI reissued.

Until June 30, 2020, there is a temporary relaxation of the rule, which allows someone in such a situation to continue to use the OCI without re-issue even if passport #2 expires and a new passport #3 is acquired before June 30 (but then passport #1 needs to be carried along with #3 and the OCI). Your family member is not in this situation since passport #2 does not expire for another few years.

Meanwhile, with all the confusion around this and variable and sometimes arbitrary interpretation of the rules by airlines, it may be best to carry passport #1 along with #2 and the OCI just in case there's a fuss about it, even though your family member technically is not in the situation! I think it would just be prudent, rather than trying your luck arguing about the rule with some airline agent mid-way through a long international journey.

Personally I have started carrying my original passport that was used for the OCI issue (my "#1 ") along with my newer passport (my "#2 ") even though I'm not required to. Just too nervous with all the reports of people being denied boarding. I spent years without carrying my original passport with me on numerous trips to India, those days are long gone, I guess.