Wait between algaecide and chlorine.

No, you should wait. Adding them at the same time just wastes your algaecide.

Chlorine is a strong oxidizer. It will break down the algaecide before the algaecide has a chance to work. You basically pour money down the drain.

The usual order: add algaecide first, let it circulate for a few hours (or overnight), then shock with chlorine. Or if you already shocked, wait until chlorine levels drop below 5 ppm before adding algaecide.

This is one of those pool rules where the label isn’t lying. Follow it.