When I bought my new bike I had a quick set-up done in the shop and thought I could tweak it as I know bikes and have the mechanical ability. Everything felt comfortable althought different from my previous bike but I changed to a compact frame (Giant) and put it down to the different geometry. 1 month of riding and I had a sharp pain in my hammy bewteen glute and knee. Mine was more pronounced at the knee but I could feel tenderness along the whole length of the tendon. Also had rest & ice, numerous bike set-ups by various learned people, much physiotherapy and am still (4 years now) battling to find sweet spot in the setup. The biggest improvement was a forward shift in the seat (5mm) so it was a substantial change. Obviously seat height had to be raised to compensate. I wouldn't think that a seat itself can cause a hammy problem but rather it's positioning. It may be slightly thicker/thinner than the previous seat making the hamstring stretch further or work in a different direction to from what it is used to. If you have had a fit, then best thing is to evaluate yourself on the bike. Feel if the hammy is stretching further than is normally comfortable. Check if your knees are not rotating in/outwards to the frame. Compare left and right legs. (I have a slight discrepency in leg left that also adds a different dynamic). Ask your riding mates what they think of your riding position,"Does it look like I am sitting too high, too low, is my backside hanging off the back of my seat, etc... Hope this helps. But best advice is to get it sorted out quickly as tendons can take time to heal properly.
