to understand the notes in the left hand you have to imagine the notes are living in a house with 2 floors above the terrain (r.h.) and 2 floors in sub-terrain (l.h.)
The middle -C- is notated on the ledger line, if you play from there upstairs with the r.h. starting with the thumb 1-2-3-4-5 you play the notes c,d,e,f,g etc. like you know. Finger 5 is now on the note G on the 2nd line of the upper staff, where the treble clef at the beginning of the staff assigns the note G. (it is derived from the letter G.)
Now if you play downstairs with the left hand starting with the thumb on the middle C the tones 1-2-3-4-5 you play the notes c-b-a-g-f. Finger 5 is now on the key F (4th line in the lower stave) corresponding to the Bass-clef that marks the note F (derived from the letter F).
As you see the scale up from the middle C is mirroring with the scale down from the middle C, thus the position of the notes is different. You have misread the notes. The note names of the scales are the same - but their position is different like it is different in the 2 ocatavas in the upper system.
I think it is a bad method to say the names in the lower system are differing a third - like you could think when you compare what is played in the video and what you thought it would be: you misread about a third, because you thought the notes have the same position in both staffs.
So you have to look up clefs, grandstaff, keyboard and scales
My advice is to derive the notes from the middle C downwards and write the note names directly in the system, extending always a third: c-b-a, when you are sure with reading these 3 notes, go on: c,b,a,g,f and then g,f,e,d,c, finally C,B,A,G:
Mind that the lower C is in the 2nd space, G is on the first line, while the lowest C is on 2nd ledger line.