As everyone knows when Druidic Staff gets additional attacks its effect for healing triggers multiple times. This is not an issue.
However, when basilisk blood is played on the staff and it is unable to attack then the effect still triggers for each attack it did not make. With the wording on cards as is there are only a few explanations possible to how this SHOULD work.
1) All Adrenaline does is grant extra attacks, not extra effects. The extra effects have to be triggered after each attack for the logic that adrenaline gives druidic 20 healing. However, even when stopped from attacking at all, it stills heals 20. That means that additional attacks can grant additional effects but loss of attacks do not effect the card whatsoever which should not be.
2) If adrenaline did grant extra turns and not simply extra attacks, it should be worded this way. There is no way for someone to know what to do without already having pre-existing knowledge of how the card works that is different from it being worded. Simply reading Adrenaline, Druidic Staff, Animate Weapon, and Basilisk Blood comes to a conclusion different than what actually happens.
3) This is either a bug and should not work this way or the text on the cards needs to be changed to reflect what actually happens. If you ask any body who has never played this game what they think will happen in that scenario simply by reading the cards I would assume none, if not just a few, would ever believe that druidic staff would still heal 20 despite having basilisk blood played on it.