I think itIt must be kept in mind that the Jewish day begins at dusk/sunset, which is the beginning of the evening. The day lasts until the next sunset. It could alternately be translated, "And evening coming, when the sun sank..." or "And evening having come, when the sun did set...."
I don't know whether this is a closing passage to the previous context (along with vv. 33-34), or the introduction to the next. It is fairly ambiguous and thus could be either. Interestingly enough, the verb meaning "to set/sink" (in reference to the sun) has a slightly different conjugation in the Westcott/Hort manuscripts vs. the Majority (Byzantine) text (ἔδυ vs. ἔδυσεν, but these are both effectively aorist active indicative / punctiliar active, so it does little to change the meaning, but should be noted).1
For clarity, itIt seems to me the following reading is best: "After evening came, when the sun had set, they brought to him all their ill and demonized." The key to understanding this passage seems to beis the context from 1:21, which is that they had just come from the synagogue because it was the Sabbath. It would have been unlawful for people to carry their sick on the Sabbath, so these people waited until after sundown to ensure they did not violate the Law. That seems to be the significance of waiting until after sundown.
1 Interestingly enough, the verb meaning "to set/sink" (in reference to the sun) has a slightly different conjugation in the Westcott/Hort manuscripts vs. the Majority (Byzantine) text (ἔδυ vs. ἔδυσεν, but these are both effectively aorist active indicative / punctiliar active, so it does little to change the meaning, but should be noted).