No surprise at all. Iran has been supplying the Shia for a long time. If for no other reason than as a response to Sunni militants been supplied out of Syria. The Sunnis remember, essentially initiated the terrorism and insurgency. At the moment it is mostly directed at the Shias.
The whole Iraq situation has moved away from the idealistic and now with hindsight, the rather naive idea that by deposing Saddam, Iraqis would embrace democracy and unite, whether Kurd, Shia or Sunni to make a new Iraq free from tyranny.
In fact, with Saddam gone Iraq is revealed as cobbled together relic of imperialism peopled by disparate and squabbling tribes which was only held together because they were all scared of Saddam. Like a lot of the middle east, Iraq is an artificial country. The borders could have been drawn almost anywhere.
In one sense, the coalition prescence is academic now. The real fight is between the Shia and Sunni and the split is a very real possibility. The Mahdi army with Iran's help probably mean to take over the south in due course. Iraq will cease to exist at that point. That's why the Iraqi government has gone to Iran. Probably in a vain attempt to stave off this possibility. I think you will find that Iranian aid to Iraq will be spent mostly in the south.
In effect, whether by means of a coup or simple evolution. The Shia south will go it's own way with a substantial part of the oil reserves.
Some years from now Iraq could be in three parts, Kurdistan backed by the USA, Shiaistan backed by Iran and Sunnistan, Syria.
At that point we can all look back and decide if the sacrifice was worth it.
