I find that all my reds are much more vigorous fermenters than my whites. I pull 3 1/2 quarts off my whites and put that in a 4 liter glass jug, ferment the balance in the 6 gallon bucket, no overflow problem (ferment the glass jug too). On my reds, I transfer the 6 gallons into a 7.9 gallon fermenter and sometimes still slightly overflow. I am not sure if the yeasts used with the reds are more aggressive or what??? I ferment my reds and whites at the same temps, usually start in the 60's and ramp up to the low 70's.
I have decided from now on, I will ferment the reds in a larger 10 gallon "Brute" until they get down to 1.020, by then the aggressive behavior is over.
Overall...with reds, get them into a larger fermenter...do not try them in the bucket they were delivered in...and even a 7.9 gallon fermenter is not big enough at times.
Good luck. Oh, my Chilean buckets are Petite Sirah and Pinot Gris.
-Tony