You do have a player window to spend the clues. The timing chart itself says:
If an action was taken, return to previous player window.
You then proceed back to:
Active investigator may take an action, if able.
At that point, the investigator is unable to take an action so you proceed.
The Details also back this up. They say:
After an investigator takes an action, return to the previous player window.
You then go on to:
If the investigator does not, or cannot take an action, proceed to 2.2.2.
So you don't completely proceed until you get to the point of having the opportunity to take an action, but not doing so or not being able to do so. That opportunity always occurs after a player window, even after the final action of an investigator's turn.
TLDR: You can spend the clues straight away.