If I’m a DSX player and in a hypothetical exemple, if I’m doing a ascending mechanical exercise , the only way to hop between strings is starting with a upstroke? I’m a bit confused at this point, thanks in advance.
If you are doing something with an even number of notes on all strings, yes. You have to start with an upstroke. That will make the last stroke before changing to the next string a down stroke and that is the rule for DSX. You could also do something where you start with an odd number of notes on the first string, then an even number of notes on all subsequent strings. The other option would be to use strategic legato if you are playing a pattern that doesn’t conform to thr above.
Also, you probably didn’t mean anything by it when you said ‘hop’, but that isn’t the best way to think about switching stings. You should have a motion that seemingly goes back and forth in a straight line (just a shallow diagonal so it goes just past thr string). The whole point is that we don’t even feel the string changes in single escape playing. An occasional ‘hop’ is the enemy lol!
What Joe said!
Actually, single escape is really powerful once one gets “in tune” with the playbook. Even number of notes per string starting on an upstroke is a big one for strict alternate picking. However, sweep and hybrid as well as legato open up a lot of other possibilities around that. An ocean of music waiting for you to dive into… 
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I would say a single pick escape is acually superior to full alternate picking. Every time I do full alternate picking it turns into me focusing on how I’m picking, rather than what I’m playing, a single pick escape shifts my foucus to the fretting hand. And whats acually being played.
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Let’s be more specific. Your pick is away from the guitar body. When you make an upstroke you come in, pluck any string that you want, and the pick is trapped between your chosen string and the one just above it. Now you have three choices:
(a) pluck that same string again, as you exit with a downstroke (DSX), and your pick will end up away from the guitar body again.
(b) pluck the string that is just above the string that you first plucked—leaving the pick trapped—this is a sweep. (It goes from trapped to trapped.)
(c) pluck the string that two strings above the string that you first plucked—leaving the pick trapped—this is a swipe. In a swipe you mute the string in the middle, so the fact that you went through it isn’t really noticed by anybody. (It goes from trapped to trapped to trapped.)
Hopefully this removes confusion vs. making it worse.