They're saying (bizarrely, as if moving abroad but keeping their currency in dollars was a realistic option anyway) that it somehow contributes to reducing the influence of the dollar worldwide.

It doesn't. It means someone bought US dollars using a different currency (more of an exchange, but the initiating party is essentially buying) and now someone has US dollars that they need to spend. Either by buying products direct from the USA, or by they themselves selling US dollars to someone else, circulating it, until eventually it is repatriated (or destroyed, physically or in value, I guess).

The way you reduce a currency's influence is by making it unstable or devaluing it, basically anything that stops people wanting to buy it or accept it as stored value.