Time dilation is an effect and not a cause. As such it cannot affect anything.
But if the objective is to "affect matter", time dilatation being cause or effect is sort of irrelevant as a mater.
A cause can affect a third parties as much as an effect, as long the cause or the effect are not occurring in function of matter.
As it is I not sure what's the correct answer except to consider "interaction" in between distinct time dilatation to create a unbalanced constant.
So my best guess, time dilatation of object A can only affect time dilatation on object B, but at the same time, on the local frame, A nor B objects can effectively affect their own time dilatation for they are the cause of their own effects.
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