According to

http://www.miata.net/cgi-bin/tirescgi

Your newer tyres (sorry US spelling - tires) are larger

Tire Size Comparison

Specification Sidewall Radius Diameter Circumference Revs/Mile Difference
185/60-15 4.4in 11.9in 23.7in 74.6in 850 0.0%
205/65-15 5.2in 12.7in 25.5in 80.1in 791 7.4%

So you are actually going further than you thought! If the 185/60 R15 size is stock for your car then the odometer will be set for that.

If you haven't had your odometer adjusted for your new tires then you are actually traveling further than you think... Look out for speed traps you'll be going much faster than your speedometer reading too! (Assuming it was good in the first place that is)