Parabolic dish focus microwave into mouth of feedhorn, how can wavefront be in phase
If the feedhorn is in the focus of the parabola then
waves reflected at any point of the parabola are in phase by definition.

The parabola (in this case paraboloid of revolution to be exact) is defined as the locus of points such that sum of distance from focus to any point on parabola and distance from such point to a plane perpendicular to beam axis is constant.

If the distances are constant (i.e. equal for any point of refelection on the parabola) then phases also must be equal.

See definition of parabola as locus of points.