bash: `set +m` option does not work when placed in the .bashrc file

If I enter the command:

set +m

at the end of the .bashrc file, when I run the command:

echo $-

the option m is missing as it should be, but...

If I enter the command:

{ sync & } 2> /dev/null

and then I press enter again without entering any commands, although I removed the m option, the output still appears:

[1]+  Done                    sync

and only when I rerun the command from the terminal:

set +m

then the output is no longer shown. In other words, this command has effect only if executed from the terminal.

The question is:

How do I make it work when placed in .bashrc file?