Arduino eeprom_put sketch writes data in two locations?
What is probably happening is aliasing.  Let's say your processor has a 16 bit address bus.  16 bits can count up to 2^16 = 65536 = 64k memory addresses.  Each address is a byte (B) so your processor has 64k-Bytes of address space.  It can physically address 64kB of memory.

What happens if you only have one memory chip with 4KBytes of memory, with  only 12 address lines?  Well, if the designer was lazy (or cost-conscious), the first 12 address lines on the processor will be connected to the 12 lines on the memory chip.  The other 4 lines on the processor will be ignored.

So it doesn't matter what the processor does with address lines 13-16 -- they're not connected to the memory chip.  Therefore the contents of the memory chip appears where you expect, starting at address 0, but also again at address 4096, and again at address 8192 and so on.