I left my war horse home, hope that's ok Stefan
Arpeggio is Italian, and means "like a harp". It is customary in guitar literature to write arpeggios with all the notes having the same duration, because it's simpler to read (and write) that way, but they are typically played so that all the notes are kept ringing until the chord changes (in this case each bar consists of a single chord, with the exceptions of bars 7 and 23 where there are two separate chords, and bar 16, where the notes do not form a chord at all). That is when using a technique called 'sequential planting', which I believe professor Delcamp uses in his video. It means that each of the playing right hand fingers are prepared (planted, i.e. lowered on a string the finger is going to play next, effectively stopping the string) just before the finger needs to play.
There is another technique that is used in ascending arpeggios called 'full planting'. It means that p,i&m (&a when used) are always prepared on the strings as one unit just before the thumb plays its note. Fingers still play their individual strings separately as indicated in the music.
Using full planting for this piece would go like this:
count just before 1: plant p, i & m
count 1: play p (alternatively i & m can be planted here at the same time when p plays)
count 2: play i
count 3: play m
count just before 4: plant p, i & m
There is a short moment when none of the strings are ringing between the plant and playing of p, but typically full plant is used when the arpeggio is very fast (it is easier to play fast using full plant) so there really isn't any pause in music. Full planting isn't used in descending arpeggios (pmi or pami), because the fingers will get in way of each other.
The sequential plant goes like this:
count just before 1: plant p
count 1: play p and plant i either at the same time or immediately after
count 2: play i and plant m either at the same time or immediately after
count 3: play m, but don't plant p until just before it needs to play, because otherwise the bass line becomes intermittent which doesn't sound good.
Now, planting immediately after the other finger has played is something that you need to learn in order to play arpeggios fast, but with slow arpeggios such as the one in this lesson, you would rather aim for planting each finger just before it needs to play, so that the strings keep ringing as long as possible. How much ringing do you want, is also a musical decision that you need to make.