Something reflexive is completely involuntary. You can't help it. You might give a reflexive scream of fright if a bat flies in your face.
The adjective reflexive has two very different meanings. Something that's done automatically, without thought, is reflexive. Things that refer to themselves can also be called reflexive, especially certain parts of grammar, as in this sentence: "I took extra time to prepare myself for the test." Because myself refers back to I, it's a reflexive pronoun. There's even a reflexive genre of writing, metafiction, which can be described as "fiction about fiction."