Since Romulus was seen as descendant of Aeneas in the Roman historiography of the late Republic, and the Iulii understood themselves as stemming from Aeneas' son Iulus, does this mean they also proclaimed they were descendants of Romulus? Because as far as I know Caesar only claimed his descendence from Ancus Marcius, whereas I can't find any evidence for a genealogical claim to Romulus...
Who told you Caesar claimed descent from Ancus Marcius? The gens Julia was one of the so-called "Trojan Families," the gentes claiming descent to the Trojans through Alba Longa. Since the tradition was that the Trojan Families came to Rome from Alba after Ancus Marcius was already king, how could Ancus be an ancestor of the Trojan Families?
Moreover, the Trojan Families could claim Trojan descent without also claiming Romulan descent. First of all, there is no tradition surviving from antiquity that Romulus had children. Second of all, since Romulus was supposed to have come to Rome before the Trojan Families moved from Alba the fact that Romulus was descended from Aeneas has no relevance to the gens Julia