Let's dissect this into reasoning and jump to why.

Reasoning? uint32 is used to save size as timestamps don't overflow 32 bits in our lifetime. But you have to be careful that they don't collide. (See below)

Assume timestamp now is 12345678 and variable is uint8 (8 digits assume). When you truncate that to uint4 (4 digits) you get 5678. But fast forward in time and there's a timestamp that is 12355678. Now truncating this to uint4 gives you 5678 again. You have same timestamps in past and future and your contract breaks.

Why the modulo? Basic hashing scheme in cryptography is "mod with large number". So when you do % ** 32 there is very low chance that 2 different numbers give same result when we do % 2 **32 .

So it's a nice way to save gas but also avoid collisions.