Connections attach to one brand. The top of /connections makes that unmissable: a brand plate reads "Connections belong to" with the brand's name in large type, and the fine print says accounts you connect on this page attach to that brand only. The switcher sits right in the plate, with the reminder: "Wrong brand? Switch before you connect."
If you arrive with no brand chosen and you can access more than one, the brand picker opens automatically before anything else. A connect can't silently land on a default brand.