HI,
These settings in the Preferences for the incoming stuff are the ones you need to look at:-

Just to restate first.
I changed my outgoing colour to that green.
I left the font as Black in text colour.
I chose Arial Black as I prefer the boldness of the text.
If my Buddies (AIM, Jabber or Yahoo) have the same Settings for the Incoming stuff as I do (Automatic) then my chosen colour shows up in their Chat with me.
They cna block my choices of Colour and Font style if they set Colours and Fonts here.
IF a Buddy is using an App that does not specify a colour or Font then the incoming messages tend to be randomised (Although there is alos a deliberate Random setting)

An iPhone does not send colour.
The colours seen on the iPhone depend if it is sending (or Receiving) iMessages or SMS.
So, AIM Buddies sending form the AIM app on PC will be in this Category of uncoloured chats.
As will Facebook Buddies posting from the Facebook page, same for GoogleTalk Buddies using their Web based Chat option on the Web Mail page.
There are also a number of Mac compatible Jabber apps and AIM clients that don't send coloured "Balloons" or the Background style you are using.
AS I have said iPhones don't send any colour or Font info in the Message/chats
Here is a pic of a Group Chats from some years ago where some are Chosen colours and some are random.

I hope this helps.

8:51 pm Wednesday; December 11, 2013
iMac 2.5Ghz 5i 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad