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We present results of the first survey of high-redshift (<z≳2.3) OVI absorption systems along parallel lines of sight toward two lensed QSOs. After a careful and well-defined search, we find ten intervening OVI systems - identified by the presence of the λλ1031,1037 doublet lines, HI, and in most cases CIV, SiIV, and CIII - and eight candidate systems for which we do not detect HI nor other metals. We assess the veracity of these systems by applying a classification scheme. Within the errors, all OVI systems appear at the same redshift and have similar line strengths in front of both QSO images, whereas in most cases CIV or SiIV show more differences across the lines of sight, either in radial velocity or line strength. We conclude that (1) the coherence length of OVI must be much larger than ≃1h₇₀^–1kpc, and (2) an important fraction of the CIV absorbers may not reside in the same volume as OVI. Given the inhomogeneous character of the data - different S/N ratios and degrees of blending - we pay special attention to the observational errors and their impact on the above conclusions. Since Doppler parameters are consistent with photoionization, we propose a model in which CIV occurs in two different photoionized phases, one large, with characteristic sizes of a few hundred kpc and bearing OVI, and another one a factor of ten smaller and containing CIII. This model is able to explain the various transverse differences observed in column density and kinematics. We apply the model successfully to 2 kinds of absorbers, with low and high metallicity. In the low-metallicity regime, [C/H]~-2, we find that [C/O]≃-0.7 is required to explain the observations, which hints at late (z≲6) rather than early metal enrichment. In the high-metallicity regime, the observed dissociation between OVI and CIV gas might be produced by galactic outflows. Altogether, the relative abundances, inhomogeneous CIV and featureless OVI are consistent with gas that has been processed recently before the absorption occurred (thus close to star-forming regions). Finally, we discuss briefly three associated systems (z_abs∼z_em) that also show OVI.