How to create a 1 hour timer with ATtiny13A microcontroller?
As the unchanged blink sketch blinks with 8.4 seconds, I think my assumption is right. The clock of the Attiny is running 8 times slower, than the code thinks.
When you have installed the Attiny core, there should be a menu entry for the clock frequency. Most likely the standard is 8MHz. But having 8MHz set does not mean, that the Attiny is using 8MHz. To choose between different clock sources and frequencies, you must change the fuses of the microcontroller (which are just some bits of special non-volatile memory in the chip, that set special hardware configuration; more information in this question). This is done, when you burn the bootloader to the chip. That's the easy version. Alternatively you can use the avrdude command directly to set the fuses. That's the advanced way.
Currently the fuses of your Attiny seem to be set to the 1MHz internal clock. But the compiler uses the frequency, that you have chosen in the menu, hence 8MHz internal clock. So the compiler thinks, that the chip runs at 8MHz and thus generates the timing code for this execution speed. But your chip is currently 8 times slower, than the compiler thinks.
TL;DR: Burn the bootloader onto the chip to let the Arduino IDE set the right fuses for your clock frequency.