There isn't a public "this" yet, so IDK. Also, Bermuda is unlikely to agree to this.
It sounds like the primary purpose here is residency definitions, which could mean that the US would be obligated or entitled to consider the Bermuda company american for tax purposes.
IRL, that Bermuda company is likely to be a shell company, receiving payment from a single client (EG msft) so that the parent company can book it as an expense.
That said, it's pretty much impossible to say anything at all before details go live, and accountants have had time to chew on it. Tax rules are all detail. Headlines really do mean nothing. "Where they do business" could mean a lot of things. Sales. employees, manufacturing, financing/listing.
Corporate income tax is applied to the net of revenues and expenses.
Some of the language in other statements seems to suggest there will be some sort of a quota system. MSFT will be defined as x% american, y% Bermudan, etc. This is pure speculation though.
Will it matter whether or not Bermuda agrees to it? It seems like their buy-in will be irrelevant, since if the company wants to keep serving US customers then they'll have to go along with the rules the US is setting up?
It will matter, because (again, totally guessing) the agreement will probably make distinctions between in-treaty countries and out-treaty. Beyond theat, idk.