Ok lets say that something very unique occurs when Volkran and Akira desire the same outcome to a given situation. This unique occurrence is something demonic and it's both of them, and neither of them at the same time. I don't wish to delve to much into what it is but it is much more powerful then Volkran is.
It uses its power to crush the angel presence within Akira, and initial evidence would show that the angel was killed, possibly to instill fear it makes out that it has killed the angel. Although with the disappearance of the sign it appears that it had suffered a rather painful exile back to heaven then actually been killed.
The presence says it's 'their secret' as neither Volkran or Akira know of its existence. Its threat was directed in that Allura shouldn't tell Akira what has just unfolded as he has know idea what happened. Hope this helps ^_^