Home country is not a well defined term*, and I doubt any digital nomad visa explicitly requires the holder to pay tax in a "home country".
However, if you are still in the tax net of a high tax country, then yes, you still have to pay tax to that country. But if you are︀ not tax resident of any high tax country (and out of the tax net), having︁ a digital nomad visa can be great. There are many digital nomad visas that dont︂ impose any taxes on the holders even if they spend 1-2 years in the digital︃ nomad visa issuing country.
*Country of citizenship, tax residence, residence and sometimes domicile are what︄ matters, and these terms are typically legally defined, unlike "home country".