It sounds as though something is causing the water valve on the side of your toilet to stick partially open. It could be that things are just dry and require some lubricant.
Some silicone lubricant works well or even Vaseline in the short term.
Here is how I access mine, your may be the same.
The pedal on your toilet rides on top of the plunger on the valve located on the side of the toilet (usually the side hardest to reach). The pedal may have a plastic cover to make it look nice. This is easily removable by removing screws on the inside. Doing so should help expose the valve which has a plunger on the top. Lubricant needs to go on the shaft of the plunger and the top of the plunger where it meets the pedal. It could be the valve is bad but your rig is new so I think maybe more likely it is just dried out and sticks.
Hope this is what it is because it is very easy to fix.
I do all my own stunts
03 Dolphin LX 6355, Workhorse W22, 8.1 vortec, 04 CR-V, Blue Ox, Brake Pro----Norm, Barb and
Doc(He's a PhD)