A.2.9 The mode-line information isn’t always up-to-date

Magit is not responsible for the version control information that is being displayed in the mode-line and looks something like Git-master. The built-in "Version Control" package, also known as "VC", updates that information, and can be told to do so more often:

(setq auto-revert-check-vc-info t)

But doing so isn’t good for performance. For more (overly optimistic) information see (emacs)VC Mode Line.

If you don’t really care about seeing that information in the mode-line, but just don’t want to see incorrect information, then consider disabling VC when using Git:

(setq vc-handled-backends (delq 'Git vc-handled-backends))

Or to disable it completely:

(setq vc-handled-backends nil)