I own two bicycles that use Ultegra 9-speed shifters. One is a compact double, the other is a triple. The shifters have 4 shifting positions. On the triple I have one position for the big ring, two for the middle ring and one for the granny. On the double I have 2 shifting positions for each chainring. I don't have dropped chain or other shifting issues with either bike. I'm pretty sure that's the way Shimano intends for it to work because I also have Flight Deck computers on both bikes and they always indicate the appropriate chainring.

Would the same set up work with other triple shifters? I can't say because I've never tried it. If it was my bike and I already owned a triple shifter I'd definitely give it a try to see if I could make it work. If I was buying new parts, I'd hold out for matching parts.