The cloud covers the mountain. Or, more to the point, it covers God's glory and from the cloud, God calls Moses.
You're just misreading the passage really - It is God doing the action (calling to Moses) and thus the locational adverbial description (from the midst of the cloud) applies to God. If it was Moses' location, then it would be: ""He called to Moses, who was in the midst of the cloud" or possibly "He called Moses to come out from the midst of the cloud" (that last is a little ambiguous in English).
Interestingly, we see a very similar passage in Exodus 3:4 (NASB),
When the LORD saw that he turned aside to look, God called to him
from the midst of the bush and said, “Moses, Moses!” And he said,
“Here I am.”
We would have to rewrite a lot, if we thought that it was Moses whom the bush cleared. The grammar is just as true in 24:16.