I've done a lot of remote work, mostly "in" EU/USA, and it's totally up to what you are agree upon. Normally, at least for longer contracts, it's normal to get paid in the employer's currency, upon pay day that value is transferred to your bank account, and some place on the way it's converted to your currency based on the current exchange rate.
But you can also invoice the company you are working for, and then do the same in reverse, except it's usually you who do the conversion on the day you invoice them.
For long contracts, more than 6 months, I would definitely take into account the exchange rate. For shorter contracts, I wouldn't care. I'm from Norway, and none of the currencies I have worked "with" changes dramatically.
But you can also invoice the company you are working for, and then do the same in reverse, except it's usually you who do the conversion on the day you invoice them.
For long contracts, more than 6 months, I would definitely take into account the exchange rate. For shorter contracts, I wouldn't care. I'm from Norway, and none of the currencies I have worked "with" changes dramatically.