Yes, if you are the business paying him, you need to file the 1042-S. You are also responsible for withholding taxes at a rate of 30% for your contractor and for submitting them to the IRS.
If you are paying remote.com and they are paying him, then no, you would not need to file a 1042-S, but you would need to issue a 1099-Misc to remote.com
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