There are several posts covering this topic in this forum, we recommend you read first.
The question you are asking has many more factors to be taken into account than just stating he moved.
Does he ever returns to El Salvador? If all ties with El Salvador are broken, meaning, he doesn't go back there anymore, has no family there (wife, children), has no assets there, no bank accounts higlikely he will be not a tax resident anymore in El Salvador.
Rule one to avoid issues is to break all ties with your previous residence (even this doesn't apply to all countries, as a
US citizen you always remain a
US tax resident)
Rule two is to be a tax resident in Chile by actually living there and paying
income tax there, keep all proof of spending (gym, local
credit card expenditures, annual rental contract, income tax bills,..). People think too easily one can become a
nomad and hence they don't need to pay tax anywhere.
Some members of this forum believe if you spend less than 180 days in a country you won't be tax resident, which is untrue. There is the term “permanent place of abode” , which is the overarching test of individual residence and applies regardless of the position under the so-called “day-count” tests, which have a deeming function in relation to residence.
Having a home or even a room in a family members house at his disposal (even never staying there) could be enough to trigger permant place of abode and being still a tax resident in El Salvador. Having children there, an
investment, paying mortgage all can trigger as his permanent place of abode and so be considered a tax resident.
Every country has different rules and if one is spending time in different countries, or has assets or income in different countries, DTA's (double taxation agreements) between those countries have to be studied and it is best a tax lawyer is consulted, especially in jurisdictions with agressive tax authorities.
This is some general information and not related to El Salvador or Chile, since I have no experience with mentioned countries nor checked if there is a DTA between both countries.