Rashi: After they brought the Aron inside. After they left, the Shechinah dwelled in the Heichal.

Malbim: In the upper world, Hishtalshelus (the order of development) descends from above to below, from more important to less important. First the world of intellect was Ne'etzal ¹ ; it is at the level of the brain. After it was the intermediate world at the level of the heart, and after it the lowly world at the level of the body. Hishtalshelus in the bottom world ascends - [first was] inanimate, then vegetative, then Chai (living beings) and then man. The Shechinah of the Mishkan was not fixed below, just it came to put honor in it from the upper world, therefore the Aron was first, for it is a semblance of the upper intellectual world. After it were Klei ha'Heichal, corresponding to the middle world, and then Klei ha'Azarah, corresponding to the lower world, to which the light descended last. Then the cloud came and covered the Ohel Mo'ed. The Shechinah dwelled in the Beis ha'Mikdash permanently. There was an ascent of the bottom world from below to above. The primary Shechinah was among the lower beings, and from there Hashem's glory is put on Shamayim. Therefore, they first put the lower Kelim, and ascended to higher levels.