‘ And the children of Judah fought against Jerusalem, and took it, and smote it with the edge of the sword, and set the city on fire.'
This may have been the lower city, or a temporary occupation of the whole. Contrast Joshua 15:63. But that was a statement of the general position with regard to the fortress of Jerusalem. Here they captured part of it and slew those within it, but their occupation was clearly only temporary. They did not have the means to fortify it, or sufficient men to leave behind to defend it, as they moved on to other victories. Thus they set it on fire.
It may be that the city was at this time only lightly defended due to the Jebusite fighting men being involved elsewhere fulfilling treaty obligations in the face of other Israelite activity. Thus when those men returned they would be able to retake it from the token force left behind to defend it. This is by no means a rare occurrence in warfare.
From now until Judges 1:36 we should note the difference between ‘smote' and ‘drove out' and ‘did not drive out'. ‘Smote' or ‘took' indicates victory but not necessarily possession, ‘drove out' indicates permanent sole possession and obedience, ‘did not drive out' indicates possession, cohabitation and disobedience. Thus Jerusalem was taken and smitten but not possessed (Judges 1:8), and later cohabited (Judges 1:21). Hebron was smitten (Judges 1:10) and possessed (Judges 1:20). Zephath was smitten and ‘devoted' (Judges 1:17). Gaza, Ashkelon and Ekron were taken but not possessed (Judges 1:18). The hill country was possessed but the coastal plain was not (Judges 1:19).
The fact that part of Jerusalem later held men from Judah and Benjamin probably refers to a situation where a part of the city was retaken at some stage but not the whole (the city was divided by a ravine), and that eventually they made their peace with the Jebusites and associated with them and lived among them, contrary to God's commands. The main fortress was formidable and was not finally permanently taken until the time of David.
Jerusalem was an ancient city under that name and is mentioned in the Egyptian Execration texts (c 19th century BC), in the Amarna letters (c 14th century BC) and in later Assyrian documents. Its name probably originally meant ‘the foundation of Shalem', a Canaanite god. But the Israelites associated it with their word ‘Shalom' which meant peace (Hebrews 7:2).