That is what you expect if you raise your insulin, insulin reduce blood glucose, so if the sweetener increased insulin without adding sugar then it reduces blood glucose.

> goes down since time passes between me starting the drink and finishing it.

Blood sugar levels are stable unless you eat sugar, they don't go down over time, unless you do something to add insulin to make it go down or add sugar to make it go up. Here it sounds like you adding insulin when drinking that and thus making it go down.