Chiffon Cake Problem
Welcome to the site @Jules. Your temperature is right and you did get rise, it sounds to me like your cake was underbaked, which is why it collapsed. When you bake a cake (or any batter) you get rise from the creation of steam, expansion of air due to heat, and leavening agents creating gas from the reaction between an acid and a base. This expansion stretches the batter, which needs to crystallize in order to retain its shape. If you don't bake it long enough the structure of the cake won't hold, and when it cools it snaps back and becomes very dense. 

The times given on a recipe are guidelines, you get different baking times because of differences in ovens, equipment, even the temperature and humidity of your kitchen. Because of this you have to bake to the result you want. The method I use for determining when a chiffon cake is done is to listen rather than touch. A chiffon cake pops a lot, it's done when the popping slows down to less than one pop per second. Firstly, don't open the oven until at least 10 minutes after the cake stops rising, you don't want to disturb it. At that point you'll probably hear lots of popping. I give 5 minutes between pop checks until I hear the popping noticeably lessen, then I check every 2 minutes. You can also use the touch test, you want the cake to spring back, but for me the pop test works every time.