Baking personal sized chiffon cake
Yes, you can use all sorts of pans for chiffon cake and it works just fine. I've made many chiffon cakes and I've never actually used a tube pan as I don't own one!
Turning the cake over is absolutely essential, and you can turn just about any pan over as long as it has a fixed bottom or one that locks into place like a springform pan. Don't use a pan with a loose slide-in bottom because it won't hold the back of the cake up when you turn it over, and it will collapse.  Fixed bottom pans can work, getting the cake unstuck from the bottom is tricky though, I use a skewer bent 90° to get underneath stuck cakes, but a springform pan is ideal as you can just use a knife.
You need to make sure that the pan is going to be taller than the cake, or that whatever you sit the rim on will not touch the cake, only the pan's rim. Chiffon cakes rise a whole lot, figure on it rising at least 3 times the batter height. Plan ahead and have it all set up for when you take it out of the oven before you start baking, you don't want to be improvising when you take it out of the oven, seconds matter with chiffon cake.
You need the cake so stick to the pan, so don't butter or flour the pan sides or bottom, or use baking paper. If it doesn't stick it will fall out when you turn the pan over, and that means it will be dense. Chiffon batter will stick to anything, so don't worry if you have non-stick pans.
Enjoy your cake, chiffons are tricky at first but they are great when they come out well!