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Presuming you had the same rated tires front and rear, the "S" rated tires that were replaced with "H" rated tires would, if anything, induce oversteer, having a stiffer sidewall. It would be helpful to know the make and model of the front and rear tires. BTW, S are rated to 108 mph and H are rated to 130 mph, not an ideal situation, but under the circumstances you and the tire store most likely were under, there weren't many options -- finding a used 195/55-15 or 225/50-15 would have been most difficult.
If the car feels unstable, I would presume that your alignment was effected, probably causing a toe out scenario in the rear. This would cause the car's rear end to follow any ripples, curvatures, etc… in the road. Going in a straight line, the difference in tire speed and load ratings would be negligible to non existent.
Aside from checking the before mentioned air pressure, also check the torque on the wheels. They should be in the 80-85 pound range.
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