Alexander was in the Caribbean islands of St Kitts & Nevis from the early 1750s, employed by Messrs Smith and Lambert, and he later married Smith's daughter. His younger brother James arrived, aged 18, in 1755 and initially both were merchants in St Kitts. They then bought plantation Hermitage in Grenada, which was managed by James while Alexander remained in St Kitts. The trading house of Alexander, James and Evan Baillie operated in St Kitts from 1770.
Alexander died in 1799.