Yes, the Westin has been a Westin since before Barony's days. And Barony was developed as a Marriott timeshare resort, not as a Starwood property.
Of the Marriott beach properties, Monarch has been around for many years, having been built in 1981 and acquired by Marriott in the mid 1980s. Grande Ocean followed in the early 1990s, with construction continuing until about 1997. Barony came next, built (mostly) in 1999. SurfWatch was the most recent addition. Those last three were all Marriott projects from the outset.