Timing of SPI when sharing common lines on independent timers

We are using two SPI masters (SPIM0 and SPMI1) inside two independently running timers. SPIM0 and SPIM1 share MISO, MOSI, and SCK. Only the chip selects are different between the two. My question is as follows:

What will happen if the timers synchronize at some point and both try to access SPIM0 and SPIM1 t the same time? Does the chip schedule the order or will there be a conflict?

Thank you

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