These pronouns are indeed used a reflexive way:
Je me lave
Tu te te trompes
Il s'évanouit
...
but it's not their only use case. They can be used too in non reflexive sentences:
Je te/le/la/vous/les remercie
Tu me/le/la/nous/les raccompagneraccompagnes
Il me/te/le/la/nous/vous/les nourrit
...
In these contexts, toi and other pronouns might be used, but only in addition and to emphasize the previous one:
Je t'aime, toi !
Il les a conduitconduits, eux !