I think all the Gopis thought Krishna was with them, through his Maya. But the Rama Avatara seems to have been earnest and straightforward throughout. As Vishnu, he should have been able to deploy Vishnu-maya to counter the Maya of Rakshasas, but he doesn't.
notes on Maya:
Maya, (Sanskrit: “magic” or “illusion”) a fundamental concept in Hindu philosophy, notably in the Advaita (Nondualist) school of Vedanta. Maya originally denoted the magic power with which a god can make human beings believe in what turns out to be an illusion. By extension, it later came to mean the powerful force that creates the cosmic illusion that the phenomenal world is real.
I am asking only about the magic power with which a god can make human beings believe in what turns out to be an illusion - advaitic Maya is something else altogether.