Are we talking TSA or CBP here?
it's CBP to initially get through border control then after you collect your luggage & line up again to hand in your blue form. After that either redeposit your bag at TBIT if tagged to final destination or take it with you to F9 checkin & drop off there.
You'd only encounter TSA once you went through the security check point at whatever terminal F9 operate out of.
Out of interest how do you know that the OP was flying Frontier? I see no reference to that in the post.
Because they'd asked a question regarding Frontier on the thread below:
Denver was also a bit of a giveaway being Frontier's home base.
I'm be interested to know how long they had in LAX in between flights as it sounds like they still made their connection despite the delayed inbound flight.