Exactly -- the diaeresis separates the two letters so that each makes their own sound.
It's sometimes used in English as well, e.g. in naïve to show that it's not pronounced like "knave" but rather like "na-eeve", or in old-fashioned spelling in coöperate to show that the first part does not sound like "cooper".
I’m not a proficient Greek speaker but I’m not a beginner either. I’ve completed the course here, all 5 levels. I can tell you that I have not seen the separation between the last letter and the exclamation mark (!) in any other Greek sentence of the course. This must be a typographical error, unless a native can tell us differently.
The two dots are a dieresis -- they serve to show that the vowel is pronounced separately.
For example, the English word naïve has two syllables na-ïve and doesn't rhyme with waive (one's rights).
Similarly here, προϊστάμενος has five syllables προ-ϊσ-τά-με-νος, rather than having οι pronounced as one vowel sound /i/.