When you use software bit banging to run a serial prototcol on some port pins ... of course a timer interrupt that is allowed to happen is going to disrupt the bit banging. If you cannot live with that behavior then you have several options.

1 - Disable the timer interrupt during the SPI communications.

2 - Disable the timer interrupt at selected times during the bit bang routines when data loss is likely to occur.

3 - Use a 2nd microcontroller dedicated to the SCI communications task.

4 - Get a separate RTC chip to be used for your clock function.

Michael Karas