I work at an oil refinery in Minnesota and in the asphalt terminal we have 5 gallon pails that hang from a top loading spout to catch dribble.  When these pails become full they're removed and placed in the rack to await pick up and removal by our contractor. During that in between time the buckets are tipped over sometimes or just leak. The asphalt tends to leak out onto the equipment or ground below. We're unsure of a good way to manage this or a permanent fix to catch the dripping asphalt and dispose of it properly. Does anyone have any suggestions?

One thing you should consider is transferring the "dribble" to a larger container, like a LABELED 55 gallon drum, until time for disposal.  Just having 5 gallon buckets of the liquid asphalt laying around violates several regulations in OSHA and the EPA.  

We have been placing HMIS labels on every bucket, pail, or 55 gallon drum we use.  Initially a year or so ago I ran into one of those EPA issues because the company I work for wasn't labeling the pails. When I discovered this I corrected that issue. However besides labeling them is there anything else I have missed that we are in violation of?

Also I probably didn't explain it that well, but where these pails sit after they're full is where I'd like to put secondary containment. I want to ensure that all chemicals are caught before hitting the ground.

I was thinking of placing poly below it and then changing it out every so often when it gets to dirty. I also thought about designing a metal vat with a drain so the asphalt or fuel oil may run down this hole into a labeled 55 gallon drum. The vat as I call will hold our full buckets until picked up. During that time if they drip they will drip into the vat and run into the barrel.

What do you think?

I think you are on the right track with the containment vat.  You have to have something to catch the drips and spills from the asphalt.  Because asphalt is a petrolium distillate you basically need to manage it like any other oil.  I really think your best option is to buy or build a larger bulk container (300 gallon) for collecting the asphalt until it is time for disposal. With one larger container, you run into fewer issues of leaks or spills than with 5 gallon buckets.  Make sure you have secondary containment at least 150% of your primary container and do everything you can to clean up your prior spills.  

One question, what does your SPCC (Spill Prevention, Control and Countermeasures) Plan, and your SWPPP say?