Today, Miller issued an apology via his Twitter, explaining what happened and that his act last night goes against everything he believes in, take a look:
To me, I don't know how spitting directly in someone's face in as accident, that being said, it seems that the two plays are on good terms after the conversation according to Dan Rosen of NHL.com
In any case, if Doughty had a problem, he wouldn't be silent about it. The NHL Department of Player Safety however, did have an issue and is calling Miller in for a hearing.