It could be that the Tiger is running on the front part of the floats. It is directionally unstable under this condition and will turn either left or right as you discribed - usually quite suddenly..

Could be a couple of causes:
-pilot technique perhaps...too much down elevator forcing it up over the step and making it ride the floats in front of the step
- floats are too short with too much relative area ahead of the step location (ie not enough afterbody to stabilize it on the water at high speed)
-too much downthrust with full power forcing the front of the floats deeper in the water. Without seeing your particular float installation, and knowing that the Tiger is very well proven design, it is possible that there is not enough positive incidence between the plane and the floats..it should be between 1 and 3 degrees positive (nose slightly high).

Just throwing ideas out that may be the cause of what you describe....without seeing your particular installation and watching the takeoff, these are only educated guesses at this point...