Hi
DSPI is the full name for the SPI used in the K64 ("DMA Serial Peripheral Interface) - it can also be called (simply) SPI.
When you send data you write the data (plus control information) to SPIx_PUSHR:

You tell the DSPI which chip select (PCS) it should use and also which attribute set (CTAS).
Therefore, in order to send (for example) the byte 0x55 - the first time with the first attribute set and the second time with the second you would write the data as follows:
SPIx_PUSHR = (0x00000000 | 0x55); // use CTAS0
SPIx_PUSHR = (0x10000000 | 0x55); // use CTAS1
Are you setting the CTAS accordingly?
Regards
Mark