Really, it's not perplexing. The connection between causation and time is that causation implies time. A cause has to precede its effect. Now why is that? Some philosophers have thought that the proposition 'A cause precedes its effect' is synthetic a priori. Others have thought, more plausibly, that it tells us part of what a cause is, so it's analytic. (A cause might be a certain juxtaposition of conditions, for example. In that case the cause and the effect could be almost simultaneous.) Still others have thought that a cause can occur after its effect. Even then, though, causation has a relationship to time. And there is the so-called "bilking" argument. If a cause can occur after its effect, all we have to do is wait for the effect to occur, and then prevent its cause from occurring. The fact that this is possible shows that there cannot be reverse causation, i.e. causation in which the effect comes before the cause. As to other dimensions - is there an analogue to causation in them? (1) Are there beagles in these other dimensions? I have just discovered that the most popular dog in Rome is the beagle, but it was a discovery, not something I could have produced an argument for. (Also the plural of "beagles" in Italian is "beagles". I thought it would have to be "beagli" - no such luck.) (2) What is our definition or understanding of causation according to which it has analogues in other dimensions?
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Causation has (has it?) an essential relation to time. If some event caused some other event, then the former was previous. But we hear from scientists that time is just one dimension of space-time and indeed that there may be (or might have been) some more dimensions, other than space and time. Should there be analogues of causation related to the other dimensions? Should there be a wider category than causation encompassing all those analogues? Isn't this all a bit perplexing?