Polyphase Analysis Filter Bank
With every polyphase filter bank I have worked with, the first block in the analysis phase is an IFFT, and the block in the synthesis phase is a DFT. These operations essentially cancel one other, so it should be fairly intuitive. Think of the DFTs acting as sinusoids modulators in this case rather than an operation to convert to the frequency domain. By having complementary DFTs, the modulation is essentially performed in analysis and then removed in synthesis. From looking at the figure in the text you linked, it appears that they’re may be a misprint, at least in comparison to my industry experience implementing this types of filter banks.

The following is a great, compact and concise resource on polyphase filter banks, multi-rate identities, and DFT based filter banks:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a457390.pdf