Adler is correct,
I usually build my deviation plans such that if I miss my connection there are alternatives to get me there in time to depart, but not necessarily 8 hours prior.
When things go wrong, or things might go wrong (ie delayed departure such that I'm scheduled to arrive 8:01 prior to show) I call CRS.
Scheduling doesn't care, in the slightest, whether you make it there 8 hours prior when you're deviating because the FAA doesn't care what you do to yourself. The 8 hours prior is an FAA required legal rest when the company schedules you, because all company scheduled transportation that's not local in nature is part of your duty day.
So, when things go awry, I call the company. Typically my arrival\final check-in has been in the 7-7:30 prior to my show. Most importantly, I'm not lying about whether I'm in place, and I'm creating the opportunity for the company to make a decision, or start thinking of a backup plan should I not make it. Moving the freight is all the company is concerned with, and if need be they can take me off the trip and do a same duty period DH to a Reserve pilot. Operational JS a pilot into the trip (seen some AM out&backs for Reserve guys to make that happen). Or grab the FedEx biz jet to get a Reserve pilot in position to move the freight.
The absolute worse thing you can do is say you're in position....and then call to say you're not going to make it. Well, the one thing worse might be to call in position and then call in sick 30 minutes prior to show when you realize you won't make it.