Last bits of config. bitstream are ignored in Passive Serial Configuration

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I don't use a host device. I use a MCU for reading the bitstream from a spi flash memory and programming the fpga.

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That's exactly what I meant with 'host'

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I see that last bits exist in the .rbf file and also in the .hexout file.

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This is a common practice. Configuration files are generated with pad bits, so that the programming device doesn't need to bother to add them.

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Also, on the PS configuration datasheet, it is written that 2 more DCLK pulses are needed after Config Done pin is High to enter Initialization Mode.

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I don't think those are really needed for CIII. From config_done to user mode (when init_done goes high), the startup sequence is driven by the internal clock, 3185 cycles required.