1st semester transcripts?

I am a bit confused.

A majority of my application deadlines are a month before my schools 1st semester ends. As such I have sent each college I am applying to my transcript through Junior year.

Should I be sending them the 1st-semester transcript as soon as I get it? Will they let me know if they want it or will they just reject my application because they didn’t get it? Will they interface with me or interface with my school if they see a problem?

Can my school send transcripts through the Common App?

Your school will send transcripts of your 1st semester when they become available even though it’s after your application deadline. This is commonplace. Whether they do it through Common App or another method shouldn’t matter to you. It’s their responsibility – you’re not involved besides letting them know which was the final set of colleges to which you applied.