Place your shirt "pie" on a couple of thicknesses of paper towels on top of a paper plate on your plastic protected working surface. It's less messy, and easy to flip the whole thing over when dying the other side. Wear rubber gloves!
Just a note: When I tie dye I usually only use three colours, Fuchsia red, turquoise and lemon yellow. With these three colours you can make any colour you like. To make the rainbow swirl shirt, imagine that your "pie" is an actual pie chart! Working from the centre of the shirt and holding the bottle low over the shirt, dye one third of the shirt lemon yellow. Do not wave the bottle around as you will make a mess! Dye the second third of the shirt fuchsia red and the final third turquoise. Do not leave any white spaces showing - the "white" is hiding within the folds! If you overlap the colours at the edges of each section you will get the other rainbow colours, i.e. green, purple and orange! It's magic!
Hint: Always put yellow - (or other light coloured dyes) on first. Once you "lose" or cover it up by mistake - it is changed to something else (either orange or green) and you can't get it back.