The detector tube contains a chemical known as a reagent. For example, in the carbon dioxide detector tube, it is the white portion of the filling, and in the oxygen detector tube it is black. When the target gas and the reagent come into contact, a chemical reaction takes place which causes the colour to change. In other words, as soon as the target gas (to be measured) passes through the detector tube, the colour changes which shows the presence of the target gas and enables its concentration to be known.

Or, to explain it in more detail:

The actual reason for the colour change is that the reagent substance undergoes a chemical reaction upon contact with the gas so that it actually is transformed into a chemically different substance.

For instance, when the white reagent in the carbon dioxide detector tube comes into contact with carbon dioxide, it is transformed into a differently constituted purple substance. Or, when the black reagent in the oxygen detector tube comes into contact with oxygen, it is transformed into a differently constituted white substance.

(There are also some detecting reagents that use a slightly different process to change colour than that described above).