3 tier steamer: Will chillies in the bottom tier make veg in the other levels spicy?
I wouldn't rely on steam to spread flavors through food. If you put chilis and ginger in one tier and meat/veg in the other tiers you will get meat and veggies with maybe, possibly a hint of chili and ginger. Many flavor compounds are oil based, and oil and water don't mix, so you aren't going to get the steam and vapor carrying your flavors around for you. Some of the oils may get airborne, but the majority of the flavor will stay with the foods. 

If you want flavor transfer in a steamer you'll need to have the food in direct contact. Sliced chilis and garlic placed on top of a piece of fish will transfer some flavors to the fish, but it's better to contain them by placing them in between 2 pieces of fish/vegetables/meat, or wrapping them up in foil or wax paper. 

Alternately you make a sauce separately and put it on the steamed ingredients after cooking.