Smallpox Griet and additional strikes

In the first round of a combat, Smallpox inflicts some hand damage on the opponent.
In the second round of that combat, Smallpox strikes: hand strike on the opponent and inflicts damage on him.

1/ Is a pox counter added at that moment?

Smallpox then gains an additional strike, and strikes: hand strike and inflicts damage on him.

2/ Is a pox counter added at that moment?

Name: Smallpox Griet
[Anarchs:U2]
Cardtype: Vampire
Clan: Nosferatu antitribu
Group: 3
Capacity: 9
Discipline: thn ANI CEL OBF POT
Sabbat: If Smallpox successfully inflicts hand damage in consecutive rounds of a combat, the opponent gets a pox counter. A minion with any pox counters takes 1 damage during his or her untap phase. Burn all pox counters when Smallpox leaves the ready region.

extrala wrote: From perspective it's clear: the cards says, during x do y. So only one counter per turn. And soon as damage is inflicted (typically during the strike resolution) in two (or more) consecutive rounds, the counter will be added (immediately).

The "during X do Y" only applies to the second part ("take damage during the untap phase"), not the first part where counters are added.