If you are serious in your query, YOU SHOULD NEVER put the seat in the frame the wrong way round. That effectively means that you are riding the rest of the unicycle backwards. The pedals, which have opposite threads to each other, will come loose and damage your cranks. This is 100% serious advice.
Back to basics. The frame has a slot at the top, which allows the frame to grip the seat post when you tighten the clamp bolt. Conventionally, this slot goes at the back. On most frames, it isn’t crucial, but it’s a convention and looks better.
Next, look at the cranks. Usually the left one will have an L on it and the right one will have an R on it. Look on the inside face of the crank (the side of the crank you can’t easily see!) and it’s usually near to the hole that the pedal is screwed into. It is absolutely vital that you have the L on the left and the R on the right.
The right side pedal has a conventional thread: clockwise to tighten.
The left side pedal has a left handed thread: anticlockwise (US = counterclockwise) to tighten.
Therefore, it is impossible to put the pedals into the wrong cranks.
You must have the left crank on the left because you must have the left pedal on the left. If you don’t then the simple act of pedalling will unscrew both pedals and it will damage the threads.
If your uni was set up correctly in the first place, and then you turned the seat round 180 degrees, the effect of that is the same as if you had set up your uni with the cranks and pedals on the wrong sides.
I cannot stress too much how important this is.
Moving on from that, why is your unicycle turning one way? I can think of 4 likely explanations.
Your seat may be at a slight angle instead of exactly in line.
The tyre (US = tire) may be too soft, which can cause a uni to squirm and develop a bias in one direction.
It may be the camber of the road. Most roads and paths have a slight slope across them to aid drainage of rainwater. This means that you are riding across a slight slope. Many tyres, even when they are at the correct pressure, tend to turn up the slope slightly. With experience, you can overcome this, but it is irritating.
You may be sitting unevenly on the saddle. Most people have one dominant foot and one weaker foot. If you are concentrating on a new and difficult skill, you may be putting too much force through one pedal.
The fact that one of your unis is turning one way and the other is turning the other suggests, but does not prove, that (4) is the least likely explanation.
Other explanations are available! Good luck.