The Player's Handbook gives no guidance.
The basic rules for falling say:
A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.
Xanathar's Guide to Everything has the answer, and it's probably up to the DM.
In the optional rules for falling in Xanathar's Guide, we see:
The rule for falling assumes that a creature immediately drops the entire distance when it falls.1
Notably, this rule is optional, or rather, an optional ruling on a previous rule, so it is between you and your DM to establish which rules you are using. Further, if you decide to use this rule, then it is still up to the DM to determine when "falling" really begins. Whenever "falling" begins, the optional rules here say that you immediately drop up to 500 feet.
I would have ruled that you fell the full distance before the end of your turn. I would make the argument that the falling began at the end of your attack action, and that you dropped the whole distance immediately. But your DM may rule differently, and you should discuss this with them.
1Note, when it says "the rule" it is referring to the rule for falling from the Player's Handbook cited in the first section of this answer. Xanathar tells us that the particular rule from the PHB assumes you fall the entire distance immediately, and goes on to give the optional rule for breaking it up into 500 foot blocks. But this ruling still appears in an optional rule section, even though it is not the particular rule being referred to as optional. It is still optional, since all of XGtE is optional. So ask your DM.