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Combat outcomes in Coriolis

I played in a game of Coriolis at DragonMeet 2018, and the way that the GM ran the combat damage system differed from my reading of it, so I want to check that I’ve understood it correctly.

As I understand it, the first success in an attack roll serves merely to generate a hit.
Any additional successes can be used to either increase the damage, or to trigger a critical (if you have enough of them).

So, as an example, if you are using a weapon with a base damage of 1, and Crit number of 2 …
If you roll 1 success, you do 1 point of damage.
If you roll 2 successes, you can do 2 points of damage, but you don’t have enough extra successes to trigger a critical.
If you roll 3 successes, you can either:
a) do 3 points of damage (1 base, plus 2 for the extra successes), or
b) do 1 point of damage (1 base), plus a critical (costing the 2 extra successes).
If you were to be lucky enough to roll 5 successes, you could:
a) do 5 points of damage (1 base, plus 4 for the extra successes),
b) do 3 points of damage (1 base, plus 2 for extra successes) and a critical (using the other 2 successes), or
c) do 1 point of damage (1 base), and two criticals (using the other 4 successes)

Is this correct? Can you do more than one critical with a single hit, if you have enough successes? And is it a choice between damage or criticals, or are the criticals in addition to the damage from the successes?

I have interpreted the tires exactly as you’ve written it. I have watched a stream that did it this way as well. Criticals always cost and you can have multiples.

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My clear understanding is that you only get one critical but that extra successes are used to make rerolls in the hope of a better critical. That what the rules say.