The event that occurred during the Second Spanish period (which generally refers to the time when Florida was under Spanish control after the Treaty of Paris in 1783 until the United States acquired Florida in 1821) is the movement of a large number of patriots and loyalists from northern states to Florida.
The Treaty of Paris in 1763 gave Florida to Spain, but that event is before the Second Spanish period. The significant battles of the Revolutionary War took place during the war itself (1775-1783) and did not specifically occur during the period when Florida was under Spanish control after the American Revolution.
So, the movement of patriots and loyalists to Florida aligns with the context of the Second Spanish period.