90's are okay for smaller tangs such as the Bristletooth tangs and Tomini Tangs, but really are not the ideal for most tangs long term. Tangs are open water swimmers, constantly moving, and most can easily grow to 8"+ in a home aquarium. This is why 6ft or longer tanks are recommended for them.
One of the main issues with your tank besides size is that Yellow Tangs can be very aggressive towards fish, especially other tangs that are added to the tank after them. This is magnetized when they are from the same species (Zebrosoma) as the Yellow and Purple are. I definitely do not recommend these two fish be put in a 90g tank. If you were to have ANY chance of this working, you would really have needed to add both tangs at the same size and time.
A hippo tang is going to grow too large for a 90g, and starting with one smaller than 3" is not recommended as they have a very poor survival rate at smaller sizes.
I'd recommend looking at a Kole tang or something similar if you really want a second tang. Other options would be a dwarf angelfish.
Ultimately, it's your tank.