I don't know the exact chemical/physical reason - but it definitely happens, with any carbonated liquid.
Presumably it's an increase in the surface area of 'places bubbles can form' which tends to be why a fizzy drink produces bubbles at the edges, against the glass it's in, around a wedge of lime, etc.
Try dropping a teaspoon of sugar in a glass of coke, or the fun one when I was a kid; stir it with a really well-chewed [real, wood] liquorice stick. Make sure you have a towel to hand. The coke will go almost totally flat inside 30 seconds.
If 'daddy owns the vineyard' then observe the same reaction pouring champagne into a dry glass.
The trick for Sodastream is to squeeze a couple more pushes of gas into the bottle first. It's not truly successful, because a home device like a Sodastream has a lower pressure limit than the commercial bottling plants do.
If you try this with a Sodastream bottle, by adding the syrup to make an actual 'bottle of tonic' be really careful pouring the syrup into the bottle; a bit at a time… again, you're either careful enough or you need a towel.
Note; you cannot re-fizz Sodastream once you have added anything other than water to the bottle. You may get away with it a few times, but eventually you will foul the mechanism.
If you're working from store-bought soda water, there's nothing you can do really.