I would like to share a part of my answer to a Quora question that was related to this topic. The full answer can be read on this page.
I would not limit the Ramacharitamansa to a single philosophy. The Ramacharitamansa is a scripture of devotional spirituality and should be compatible with multiple philosophies, including Advaita, Dvaita, Visistadvaita, and others . For living beings focusing on the lotus feet of Lord Rama, philosophical differences should not matter too much.
We can find nondualistic elements in the scripture and dualistic ones as well. If someone sees Advaita in the Ramacharitamansa, he or she is correct; if another being sees Visistadvaita, he or she is correct as well. Goswami Tulasidasa has been one of the pioneers of Hinduism as far as amalgating opposite viewpoints is concerned.
 This can also be said about the Bhagavad Gita, which has had both dualistic and nondualistic interpretations depending upon the devotional and philosophical preferences of spiritual seekers.