Because it draws those “pixels” as the signal reaches the monitor. When half of a frame is transmitted to a CRT monitor, it’s basically half way done making it visible.
An LCD monitor needs to wait for the entire frame to arrive, before it can be processed and then made visible.
Sometimes the monitor will wait for several frames to arrive before it processes them. This enables some temporal processing. When you put a monitor in gaming mode, it disables (some of) this.
But they do need to suspect it.
If they find an encrypted blob, ask for the decryption key, they decrypt the data and analyse the decrypted data, then they may not suspect that a different decryption key will reveal a different set of data.