Does Genji get ult from healing?
No, even if Genji can heal by deflecting heling projectiles, he doesn't gain ultimate charge from it.
Short answer: No.
Long answer:
All heroes gain ult over time and from doing damage.
However, they also get additional ult from actions that are specifically flagged as doing so, usually from using their abilities.
As a general rule, only healers gain ult charge from healing players.
In fact, one change they made in Patch 1.20.0.3 was to make Sombra no longer gain ult when others use her hacked health packs.