Does the Eldritch Knight’s Eldritch Strike feature impose disadvantage on a saving throw against a spell cast before the attack?

Consider the following scenario:

A level 10 Fighter with the Eldritch Knight (EK) archetype (PHB, p. 74-75) is facing a single opponent, and has hold person as a spell available.

  1. EK attacks with both attacks available. If both miss, they try again next turn. If either hits, Eldritch Strike (the level 10 archetype feature) triggers against the target, and EK will proceed to the next step.
  2. (a turn passes)
  3. On EK’s next turn, they cast hold person on the person targeted previously. The target has disadvantage on the save due to Eldritch Strike. If they still pass, EK goes back to square one. Otherwise, EK does the following:
  4. EK Action Surges (Fighter level 2 ability). They use the Attack action to get two attacks with advantage against the target. If either hits, it does critical damage (thanks to the paralyzed rider on hold person), and Eldritch Strike triggers.

The wording in Eldritch Strike is as follows:

When you hit a creature with a weapon attack, that creature has disadvantage on the next saving throw it makes against a spell you cast before the end of your next turn.

Does the target have disadvantage on the save against hold person it makes at the end of its next turn, even though hold person was cast before the triggering of the Eldritch Strike event that would impose disadvantage?