Reverse faults are, in fact, the reverse motion from normal faults. Instead of a stretching stress, reverse faults form because of compressional stress. Rocks are squeezed until they rupture, forming faults, on which there is movement to "slide over" rocks on one side of the fault toward the other.
And, the effect on drilling for oil is also in reverse for reverse faults. Instead of the possibility of totally missing a target stratum, an oil well can encounter a given stratum twice within the narrow zone of overlap: