Okay, so I got it now. Instead of
var tinydropdown = new TINY.dropdown.init("tinydropdown", { ... });
you have to use a single variable name (not an array) for each instance:
var tinydropdown1 = new TINY.dropdown.init("tinydropdown1", { ... });
var tinydropdown2 = new TINY.dropdown.init("tinydropdown2", { ... });
var tinydropdown3 = new TINY.dropdown.init("tinydropdown3", { ... });
regards,
Mario