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In this paper, we consider uniformly accurate methods for solving the highly-oscillatory Vlasov equations with non-homogeneous magnetic field. The specific difficulty (and the resulting novelty of our approach) stems from the presence of a non-periodic oscillation, which necessitates a careful ad-hoc reformulation of the equations by using a confinement property of the solution. A two-scale numerical scheme is proposed where the error estimates show that our scheme not only remains insensitive to the stiffness of the problem in terms of both accuracy and computational cost, but also preserves the confinement property at the discrete level. Our results are illustrated numerically on several examples. [ABSTRACT FROM AUTHOR]