From your reference “The German-speaking Swiss(Deutschschweizer), i.e. Alemannic...

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From your reference “The German-speaking Swiss(Deutschschweizer), i.e. Alemannic German , historically amalgamated from the Gallo-Roman population and the Alemanni and Burgundii , including subgroups such as the Walser ” (and “Alemannic German” is a pleonasm : in their own language its Alemannisch )

So you must go back about one millenia to find connections between Swiss German and modern Germany, and it’s not related to emigration or colonisation