That's actually correct!
Note that Teacher says
"At the start of your turn, you may call this,..."
There is no "next" in it, and the text is "below the line", so it happens not when you play this, but some other time.
A rule, which you may not be familiar with, says that if a "Start of turn" effect creates another "Start of turn" effect, the new "Start of turn" effect happens already this turn.
You can't get this speedup by playing Teacher "normally", because then the "Start of turn" is over for that turn, so the first opportunity to call it is your next turn. But a few effects can play cards at the "Start of turn" (Ghost, Captain and now Delay).