No, not on all things. Divine providence imposes necessity upon some things but not upon all (as some formerly believed) because to providence it belongs to order things towards an end, but after the divine goodness, which is an extrinsic end to all things, the principal good in things themselves is the perfection of the universe, which would not be, were not all grades of being found in things, whence it pertains to divine providence to produce every grade of being.
The effect of divine providence is not only that things should happen somehow but that they should happen either by necessity or by contingency.
Therefore whatsoever divine providence ordains to happen infallibly and of necessity happens infallibly and of necessity; and that happens from contingency, which the plan of divine providence conceives to happen from contingency.