Certainly looks like
Cupaniopsis anarcardioides and you're right even in less than ideal conditions this tree can develop significant spread from the loww scaffold limbs 6-7m across easily.
The photo is of one of the widest specimens I've ever seen in Melbourne Botanic gardens
DSCF6749.JPG
So I'd absolutely agree with Ekka's recommendation for directional pruning, the earlier the better for you and the tree.
SF