My question is how come two avatars of Vishnu (Rama and Parasuraman) can be in the same place in the same time ( Ramayana ) ?
Srimad Devi Bhagwatam Mahā Puranam 5:1:12-54. says thus.:
12-54. Vyāsa said :-- “True it has been said by you that Vāsudeva the Janārdana, is the destroyer of the Daityas and He is able to create and preserve the Devas and do all other acts for them. But the Great Lord assumed a human body; therefore he had to perform his duties like a man and observe the Varṇa and Āśrama Dharmas pertaining to human beings. . . . Again, the Ṛṣi Nārāyaṇa is the part incarnate of Viṣṇu, and Vāsudeva is the part incarnate of the Ṛṣi Nārāyaṇa; hence what wonder is there, if Vāsudeva be seen to adore and propitiate Śiva? Śiva is the God of gods; and He is the Lord of all the causal bodies that exist; in the state of Suṣupti (deep sleep). In this respect, Śiva is the creator of Viṣṇu and Viṣṇu worships Him in this light. Rāma, Kṛṣṇa and others are all part incarnations of Viṣṇu; so there is no wonder if they worship Śiva......."
Avatars of Lord Vishnu meeting other avatars or avatars meeting Lord Vishnu the avatari himself is not a new concept. Lord Rama Saw Lord Vishnu, Lord Krishna and Arjuna (The Nara Avatar) also met Lord Vishnu. Lord Bhargava Parshu Rama and Dasharathi Sri Rama met each other. The verses are given in this answer of mine.
I hope this clarifies all your queries. Prd..