Vim Ignores Aliases

If you want a word for the notification itself, try "reminder", "alert", "notice", or "warning bell".

If you want a word for the time period itself (which I think is what you're asking), that could be a "pre-event period", "notice period", or "reminder period". (I can't think of a single-word term.)

Vim 'ignores' your aliases because your shell is not in a 'mood' to parse your .bash_profile/.bashrc (you did not specify, where your aliases are defined) because it is not started as a login/interactive shell (read here to find out more about what is read when and for what reason).

So, you have several options:

1. Put the code you use in your pdflatex alias into a script and call that
2. vimrc: 'set shell=/bin/bash\ -l', put your aliases to .bash_profile
3. Call your shell as an interactive/login shell: :! bash -l -i -e 'pdflatex .'