The scorch marks in the images provided appear to be condensed wood sap, common with laser engraving. They can be completely eliminated outside of the burn area by using a mask, typically ordinary masking tape. I use sign cutter transfer paper high tack as a mask as it requires less laser power for burn-through.
The scorch marks outside the engraved area is wood sap. The coloration inside the burn area is also wood sap, but is affected by the type of wood.
I've engraved laser-grade plywood, which has a "laser-friendly" concentration of binding glue holding the layers. Using wood that is engineered for routers does not exclude its suitability for laser use, but does not guarantee results.
Another product commonly used with laser cutter/engravers is MDF, which is effectively sawdust and glue. The glue burns/vaporizes and condenses as well.
The type of wood will play a large factor in the coloration. It may be necessary to experiment with various species of wood samples in order to find the red hue you seek.
Lower travel speed of the laser along with appropriate power settings for the desired depth of engraving will provide more sappy burns. Reducing the nozzle air flow with an add-on valve will increase the sap deposited. If you reduce nozzle air flow, do not reduce it to the point where the vapors will travel into the nozzle and fog the lens.