Well, I'm sorry to say this, (flame suit on), but you should NOT have been giving space for anyone to enter there from a"suicide" lane.
They should wait there until THEY know it's safe for them to turn. This was an accident waiting to happen. There are three lanes for them to cross, not just yours, and you are letting them through where they are blind to see??? Now if it were a street intersection where it is illegal to block, that is a different story, but giving ROW to someone who doesn't have ROW is asking for trouble. I see this thing all the time where people creep through crowds of cross traffic just asking for trouble!
I learned the hard way back in the 80's when turning left out of a fast food joint with a stop light sveral yards to my right. The folks were being "nice" in letting me out through 2 driving lanes, but when I got to their left hand turn lane a limo had gone around the stopped traffic and yellow lines to get to the green arrow in that turning lane and, BOOM", T Boned me in the drivers side. Luckily for me I was OK and the limo driver was at fault for being on the wrong side of the road, but still it was a chance I shouldn't have taken and would have been better off waiting for my safe turn out. If everyone followed the rules and stopped being nice, we'd all get there safely!