Channel inserts on a mixer act as both the input and output when connecting outboard gear, like compressors. The "tip" of the cable is used as the send from the mixer and the "ring" acts as the return. Using a standard 1/4" TS or TRS cable will not allow the signal on the channel to go out to the recorder while at the same time feeding through the rest of the channel. Without that return signal on the insert the signal gets broken through the channel and only gets sent to the recorder.
In order to use the inserts as direct outputs you will a cable called a Insert Direct-Out adapter. This will have a 1/4" TRS jack on one side and a female 1/4" TS jack on the other. This adapter allows the signal to flow to the female output jack but also reconnects the signal back to the "ring" in order for sound to still be heard through the channel.