There's a huge arguement about this on TWF, so I won't go into it too much here. Suffice to say it wil depend entirely on the wording of the Thundertusk's special rule.
However, if you're asking for an opinion, then I think they should strike in initiative order. They can ignore the ASL from their GWs thanks to their rule, but the Thundertusk's application of it could not be ignored. As I say, this is just my feeling on the matter and not fact.